I won't be in this position, as my parents were planners and my mother is comfortably retired. My MIL we have no idea, but she's demanded non-monetary support and been turned down flat (bad history there - husband is still mulling if he ever wants a relationship with her again at this point).
If your mother is asking for your help, then the only way I would consider doing anything is if she lays it all out completely. All of her bills, her debts, her income and pensions - everything must be discussed. Once you see the whole picture, it makes it a little easier to figure out what can be done by her and what you feel comfortable providing. For instance, if she's blowing hundreds every month on cigarettes and lotto, then I'd be much less inclined to do anything (not saying that is this situation, just a for instance).
If she is remotely capable of some kind of work, then she should keep working. If she could live off her pension, but only if she sells her house, car and lives like a monk, then maybe, but that's where the emotional connection and familial responsibility "gray area" kicks in. If you have a close relationship and want to help her out, then there are ways to do so - pay a few of her bills (directly, no cash to her) or otherwise subsidize her to the best of your abilities without endangering your own family's wellbeing.
If the parent was a spendthrift and I had a rocky relationship, then I would not be inclined to help out except as a one time thing if that.
I don't believe that having a blood relationship should make you beholden to a person. The actual interactions means more than blood to me, and if there isn't fondness or even a little respect on both sides, then the "relationship" is purely a matter of coincidence that you're related to said person and that doesn't make you responsible in the least if you're both adults.