With a lot of states having issues regarding unfunded teachers pensions, I was wondering why it doesn't ever appear to be a main point of their lobbying/protesting/striking. Wouldn't it be in their best interest to push for getting it stabilized?
If the pension is un/underfunded, that's not the union's problem.
The money that is supposed to be in the pension was generally decided on previously by negotiation between the union in the district. Once both sides have signed the contract, it is the district's responsibility to hold up their end of it. This includes paying any pension contributions it owes. How it goes about doing so is its own problem. Usually this involves setting up a fund to invest money to earn some income and smooth out payments/payouts, since future costs can be predicted, but it doesn't have to.
Since the district is contractually obligated to pay the teacher pensions, it doesn't matter whether the fund set aside for that purpose is sufficiently funded. It is obligated to make up the money from elsewhere if the fund doesn't have enough. Of course, there might not be enough money in the pool to do so, but that's another problem.
This flexibility is what enables a district to "raid" the pension fund to pay other obligations - it's just money set aside for teacher pensions, it's not theirs yet.
Thus, unions don't have any reason to spend any bargaining power trying to force their district to do what the district has to do/should have done already.