Hi Brian,

Good question, and the short answer is that it depends on which payment plan you chose.  But first, let me address the assumption in your question - the loan balance hitting zero equity is not what stops the payments.  That is an important distinction.

With a tenure payment plan, the lender is contractually obligated to keep sending you monthly payments for as long as you live in the home and meet your obligations - taxes, insurance, and maintenance.   Even if your loan balance eventually exceeds the home's value, the payments continue.  That is exactly what FHA mortgage insurance is designed to cover. 

Payments only stop if you stop meeting the loan requirements - you move out, fail to pay property charges, or let the home fall into disrepair.

Here is how each payment option works:

Fixed rate - lump sum.  You receive everything at closing in one payment.  There are no ongoing monthly payments, so the question of payments stopping does not apply.

Tenure payments.  Monthly payments for life, as long as you occupy the home and meet your obligations.  This plan is designed to address exactly what you are asking about.  An equity drop to zero does not stop the payments.

Term payments.  Monthly payments for a specific number of years you select.  When the term ends, payments stop.  This is one where payments can end while you are still alive and in the home.

Line of credit.  You draw funds as you need them.  The unused portion of the line grows over time.   Once the available balance is exhausted, no more draws are available.  You remain in the home as long as you meet the loan requirements.

Modified tenure. A combination of lifetime monthly payments and a line of credit.  Because a portion of the principal limit is set aside for the credit line, the monthly payment amount is lower than a straight tenure plan.  The monthly payments still last for life.

Modified term.  A combination of monthly term payments and a line of credit.  Payments stop when the term ends.

To directly answer your question - yes, payments can stop before you die if you choose a term or modified term plan.  If you have chosen or are considering tenure or modified tenure, payments do not stop for equity reasons.  They only stop if you no longer meet the occupancy and property charge requirements.

Reference: HUD Handbook 4000.1, Section II.B.3.e - Payment Plans (PDF pages 595-596).