I think if PAR were in any kind of trouble there'd be an asset selling spree long before the company were ever put for sale. They have a number of chips to put in play.
1) Its CT lines. Frankly it would make good business sense to put those open to bid right now since their interest in serving that market is about nil, and with them seemingly relegating the Conn River Line to a mostly PAS service it's getting further and further out of the way for them to go south of Springfield. CT would certainly buy the Highland, PAR's portion of the New Departure branch/Terryville Loop, and the tiny active portion of the Canal Line to consolidate the last contiguous lines (excepting the self-sustaining NECR and P&W mains) not yet locked up under gov't control, and hold it as a long-term commuter rail option. CSO, CNZR, and Naugatuck would almost certainly bid on the trackage rights since it's valuable territorial expansion for them and would give them new interchanges. Plus there's more business to be had by putting in something better than the eighth-arsed effort PAR did, and CSO and CNZR in particular have been pretty aggressive about signing on new customers. It makes no sense for a Class II to own and operate those lines. It makes a lot of sense for a plucky shortline to do it on state-owned track.
2) Marginal branchline dump. Not that they have many left, but there's still a few low-margin lines they still own where flipping them to the state for ownership consolidation would relieve maintenance and tax costs. Talking a motley low-mileage assortment like these: South Reading Line in Peabody, Medford Branch, OOS Moran Terminal lead track, Adams Branch, Lawrence and Westford industrial tracks, OOS Lowell industrial track. Maybe the Nashua-Milford trackage in NH since the state already owns the line from Milford-Newington. State of MA has pretty much locked down every other ROW under public ownership save for the freight-only Class I/II/III mains (PAS west of Fitchburg, CSX west of Worcester, NECR, P&W's twin mains, Housatonic), the Class I/II interchange branches (CSX Framingham Secondary, CSX Agricultural Branch, PAR Worcester Branch, Conn River Line), and the shortline mains (G&U, PV) where those are the tiny operators' main hard assets. They've already got an agreement in principle to take the Watertown Branch off PAR's hands whenever they can get Newlyweds out of their contract. They would certainly be willing to offer a package deal for all these stubs that a major buyer like NS would have zero interest in owning...both to keep the viable ones (South Reading, Adams) operating and to preserve the ROW's that are going by the boards. You'll probably see more of that even if PAR is healthy, as the state strategically wants things like the Moran terminal track and I certainly can't see malformed stubs with hardly any business like Medford staying active much longer.
3) Passenger asset consolidation. The T is most likely going to snap up the Wachusett extension of the Fitchburg Line sooner or later. It's their MO to own every single piece of track they run on, and the 5 miles of new extension is currently foreign territory. They already paid for trackage rights on the Worcester Branch as a long-term hold. I could see them taking it a step further and eventually buying even with a healthy PAR just because it's a dual Class I/II interchange branch critical to the state freight rail plan. If PAR can't be compelled to get the speeds up, the state certainly will and will broker more traffic from CSX to make it worth everyone's while. Certainly the Conn River Line is a strategic asset. Amtrak much prefers running on gov't-owned track, and that's a significant piece of NEC-branchline infrastructure to reel in. Not to mention there's a whole lotta business the state can drive on it by negotiating directly with NS and giving PV a little more leeway to fill the local vacuum PAR is leaving. Amtrak, NHDOT, and MEDOT would probably take the hit to buy up the Western Route to Brunswick. MEDOT already owns everything beyond to Augusta if they're hedging on still more Downeaster expansion. NHDOT would certainly buy the NH Main to Concord where the MBTA has already secured passenger rights in a prior deal. For all their squeamishness about passenger trains NH has also been excellent about snapping up ROW's. They own just about everything non-PAR except for NECR's short in-state jog and the mains for the St. Lawrence & Atlantic and NH Northcoast shortlines...plus have everything abandoned in the last half-century landbanked under state control. PAR's ownership of those two critical trunklines, plus the Eastern Route/Hampton Branch (required to be reactivated to Seabrook in 20 years for decommissioning of the nuclear plant) and the Portsmouth Branch are ones they'd flag as very high-priority purchases.
4) Real estate. Certainly any abandoned lines they may still claim land ownership on would be up for a pennies-on-dollar dump, if there are any left. But they still own a good deal of former yard property. Nothing of Northpoint caliber, but I'm sure they'd broker off what they had because yards are nice big parcels and often had towns grow up around them so surrounding population density makes them attractive redevelopment choices. CSX is a quasi- real estate company with how it staggers out asset sales for a price premium. It's still got a number of holdings in the northeast to milk for future sales, and the states will overbid to secure those RR properties.
5) Mainline. NS would obviously want all of the non-passenger portion plus Ayer, Gardner, Mechanicsville to itself. I think there's little doubt about that. They might even be willing to go to Lawrence as an east-end interchange if they're not keen on operating the MEC and want an exclusive interchange. Would be a little easier to manage traffic if they had Lawrence so some interchanges don't have to plow against passenger traffic all the way to Ayer.
Only lines I think would be dicey are the MEC branches. Southern New England I think the states would probably welcome it if they left, NS took over full-time and actually maintained the main, and the shortlines got turned loose to stimulate better business up and down the CT River. But it really would be problematic for Maine if the company destabilized; that's the one place they aren't indifferent to business and do still hold sway a portion of the local economy. MEDOT also lags all other New England states in public ownership of the in-state ROW's, and there's an awful lot of PAR trackage up there outside of the northern extent of viable passenger rail that would be thrown into doubt. Although MEDOT's insistence on reactivating low-margin branchlines seems to indicate they'd try even to the point of overreaching to assist the MEC system in staying active and intact. As long as the paper mill business is stable and there's a Class I to interchange with south, I think a regional operator could step into the vacuum and serve the system. Whether it would be profitable long-term without the state overleveraging itself is anyone's guess. Either that or some spun-off residue of PAR could become a 'new MEC' Class III operator, just own that trackage, not work any locals outside of a ME/NH base, and only retain overhead rights in MA for interchanges. If all track outside of Maine's borders and on any passenger routes went under full state control, with NS taking over the Patriot Corridor, then the remaining MEC trackage is manageable-enough mileage for a modest-size private operator to maintain at 10 MPH PAR standards. PAR's track dept. capacity fails them when they have to break a sweat maintaining better-than-Class-1 speeds on PAS, Conn River, Worcester Branch, and the Western Route in service to its recent passenger and interchange deals. Put all that under the exclusive jurisdiction of the states and dump all those far-flung Southern NE tiny branches and it's really not gonna be a big deal to maintain the MEC.