My wife is a h-4 visa holder and has no ssn yet since I am still h-1b status.she was hired to be a private duty nurse in the house taking care of an old lady with alzeihmer's disease working 8hrs/day without asking any social security.the husband is regularly paying my wife every weekend by check and putting her name on the check and the money that they pay to her is being re-imburse from their insurance that covered them. I know it is not allowed to work here with an h-4 visa, what is the risk involved in this situation. The husband is saying to my wife that there is nothing to worry since he did not ask for her social security.Is is safe to continue the job?

IRS don't care much about visa or employment authorization. Anyone who stays in US longer than 180 days in a year and makes over $600/year needs to report income taxes.

You can apply ITIN for her. File W-7 form with your federal return.