Typically, your benefits don't go to anyone. However, if you have eligible dependents, THEN they may be beneficiaries to Social Security Insurance that stem from your work record. But no, your own benefit doesn't, per se, go to either.
That said, a child can get a dependent benefit in an amount of up to 75% of a deceased parent's primary insurance amount, while a spouse, if 1) raising a child under 16 of the deceased 2) or over 50 but disabled or 3) over 60 -- can be eligible for a 'widower' benefit (survivor benefit) o f71%-100% of the deceased spouse's PIA or benefit amount (depending).
Now, if the child files for an is approved for such a survivor benefit, but he is a minor and considered unable to handle his own money to pay his own bills, there will be a Representative Payee obligated to be assigned for that purpose. It is typically the other parent if raising that child, since he is in the best position to use that money for the child's needs (food/shelter, etc., or savings, if the child's needs are elsewise met). He can not use it for himself and generally must provide the SSA an "accounting" - although that is often a vague requirement when it is a parent. The husband's own receipt of benefits, if any, are his own, and of course he can do with them what he wishes. Your own benefits cease to exist, since you must survive a whole month to be eligible for any month thereafter.
If you have no minor children, or no children disabled before age 22, and no dependent spouse (as defined by the SSA law), no one will have any benefits stemming from your working record and SS insurance.