They can absolutely go after you, but its like any debt collection situation, it might not be worth it for them to do so.
The problem will come about if there are huge numbers of defaults, which if the season continues like it could now, will happen. If you stop paying, the tickets become the property of the jets, and if they cant resell the PSL or resell the individual game ticket, woody will have to "buy" it to avoid a blackout.
The team has been able to avoid blackouts now because most of the unsold seats are the cheaper ones in the UD and they lowered the price so that in the event they need to buy them in the blackout scenario, its cheaper.
If woody needs to starty buying lower level seats, its a real problem.