Tell him to immediately file police complaint for the same for his protection 

Emotional blackmail involving suicide threats is a heavy burden, and it is completely understandable that your relative is scared and that the family has lost its peace. Please tell your relative that he does not have to stay silent out of fear.

Advise your relative never to dare her, mock her, or fight back aggressively when she threatens self-harm. He must remain completely calm, walk away, or record it passively.

If she has genuine mental health struggles, document an attempt to take her to a psychiatrist or counselor. If she refuses, keep a record of that refusal. It proves the husband tried to help her.

He should consult a competent criminal defense or family law advocate immediately to draft the police complaint correctly. Taking charge legally will give him his peace of mind back.

File police complaint of relative constant threats to commit suicide 

rely upon audio recordings ,messages exchanged with relative

1. Let him inform the jurisdictional Police Station that his wife is blackmailing him of suicide and he shouldn't be held liable in case she commits suicide.

2.  Let him take her to psychiatric counselor to counsell her not to go to the extent of committing suicide.