What is the name of your state (only U.S. law)? california
my and i are getting a divorce. my wife was an immigrant when i married her. we have been married for 4 1/2 years and she is now a US permanent resident. currently, doesn't have job. i am legal sponsor for her based on the immigration paper i had to fill out or once she became a permanent resident that responsibility is no longer mine?
The responsibility is yours until one of these things happen:
She dies
She leaves the country permanently
She becomes a naturalized citizen
She has earned enough qualifying social security credits (iow, worked for about 10 years).
Divorce does not end your obligation either.
Worst case scenario? She sues you for support using the I-864 (and so far the courts have consistently ruled in favor of the immigrant) and you're on the hook for support up to about $1000/month. Theoretically this could be for the duration of her life (believe it or not, if YOU die she does have standing to sue your estate, although there have been no published cases of this happening yet).
(example: if she is not working, you get to pay the full amount, which is 125% of the federal poverty level guidelines. At least one court has ruled that the immigrant is not obliged to mitigate by finding - or at least searching - for a job, which does seem quite unfair to the sponsor. Similarly, if she earns say $600/month, you're only responsible for the remainder - about $400/month.)
Best case? You are very nice to her and offer to pay for her to become naturalized; she gets many benefits from this (she'd be able to get state aid for one thing) and you will no longer be obligated to ensure support. If she's genuinely broke she might just jump on that...but as with everything else, there's never a guarantee.
ETA: LdiJ is absolutely right - the immigration situation is perhaps the single most critical factor in your case; it can change absolutely everything. Everything. And we're not exaggerating here.