UA should be able to cancel the flights but keep the ticket, which will mean that the value stays with the ticket for you to reuse at a later date. They normally wouldn't do this for a fully refundable ticket, but they certainly can.

However your description of the situation does raise some interesting legal questions about who really owns the ticket. Obviously it depends entirely on the exact situation, but are you confident the ticket (or the funds from it) is really yours to use??