Your husband's sister needs a full mental health evaluation if she does not have a doctor. If this is true and she does not have much fund, being sure his parents know where an uninsured or low income person in their community can go for a MH screening might help. If she does have a doctor, then encouraging her to get an appointment to discuss any changes in her life. If she is on medication and not taking it, this could also be a cause for the downturn.
In any case, I agree you do not just give funds blindly. You could tell her that you would pay for her to go to see her present or new doctor and/or medication if you are able to do so for a period of time till she gets back on her feet Getting her appropriate medical care is really the key to her turning her life around. Would she qualify for Medicaid health insurance coverage or under the new Affordable Care Act if she lacks health insurance. If so, helping her to sign up by the March 31st deadline is important.
In terms of finances, I would not send her money as it would just go down a blind hole. I would see if she qualifies for any benefits through the local Department of Social Services including: TANF, SNAP (Formerly Food Stamps) and/or any other services. Another thought would be to see if she needs assistance applying for Social Security Disability Insurance - SSDI if she has worked in the past and would qualify for this financial benefit.
If she refuses any and all suggestions on getting help with her present mental health issues and/or applying for financial assistance, then as you may have the means to do so, you might ask her for direct information to pay her rent bill or basic utility bill for a given period of time. Similarly, you could buy her a gift card for a local food store weekly for a period of time. But to be clear, things will not improve greatly unless your SIL is able to take a first step and realize she needs help.