Since no one has answered this question directly, I'll give it my best shot.
As I understand UAIR's fragmentation policy, if more than 15% of UAIR's assets are sold, UAIR pilots must be transferred to the successor. I'm not sure if 15% of the pilot list would transfer or if 15% of the active pilots on property would transfer, or (most likely) some smaller percentage of pilots would transfer.
The UAIR pilots would be incorporated into the successor's seniority list in accordance with the ALPA Merger & Fragmentation Policy and Allegheny-Mohawk Labor Protective Provisions.
Keep in mind that UAIR's aircraft are unlikely to be acquired; it's more likely that they'll be returned to the lessor, parked in the desert, and only then will another airline have interest in the planes. The policy is more likely to be triggered from the acquisition of gates, slots, and routes.
If I understand everything correctly, the fragmentation policy is voided if UAIR declares chap 7 because it is no longer an ongoing entity. However, I would suspect that UAIR will end up going chap 11 and will survive, whether at its current size or something smaller.
The sticky point, as illustrated by yourself (motnot) and autofixer, is how those pilots would be incorporated into the successor's seniority list. ALPA's Merger & Fragmentation policy specifically addresses career expectations. The most likely outcome of any pilots who would be fragmented is that they would be placed at the bottom of the successor's seniority list ('stapled'). The acquiring airline's pilots are likely to demand management to staple any UAIR pilots to the bottom of their seniority list, with the possibility of minor dovetailing (dovetailing is when you have a ratio of, say 50 pilots currently on the seniority list to one pilot of the acquired; the first 50 slots go to current pilots the next one goes to acquired pilot, next 50 to current pilots, etc. This can be modified by stating that the top acquired pilot is #1000 on the seniority list).
Taking more pilots onto the acquiring airline's seniority list when there are already pilots on furlough will create a lot of internal problems; the acquiring airline's management will probably require UAIR's MEC to waive any lawsuits stemming from seniority integration issues.
Consider the case of AMR bidding for all of UAIR's DCA gates and slots. It would most likely trigger the 15% of assets rule. AMR already has 1356 pilots on furlough, with another 123 to be furloughed on 1 Oct 2004. You can bet that AMR's pilots are going to be ticked off if any UAIR pilots get put in front of furloughees. The same goes for UAL with 2172 furloughees, DAL with 1020, NWA with 789, CAL with 513, etc.
This is a very ugly topic; I hope that UAIR is able to hold together and make things work out.