What happens after a death if a person has no will or no family?

DSturgeon, dying w/o a will is considered an "intestate" death.   States have their own hierarchy of heirs in this situation.  If the individual is in KY as you profile indicates you are, these laws of succession would apply:

https://www.nolo.com/legal-encyclopedia/intestate-succession-kentucky.html

Provision is made for someone w/o family:

"If you die without a will and don’t have any family, your property will 'escheat' into the state’s coffers. However, this very rarely happens because the laws are designed to get your property to anyone who was even remotely related to you. For example, your property won’t go to the state if you leave a spouse, children, siblings, parents, grandparents, great grandparents, aunts or uncles, great uncles or aunts, nieces or nephews, cousins of any degree, brothers or sisters of grandparents, or the children, parents, or siblings of a spouse who dies before you do."

Are there any relatives at all, even very remote ones?

No family at all? Do they have an estate, assets? This would be a good question for Probate. If no will an Administrator could be assigned not sure if it has to be family. That person would have the responsibility of the Executor. But instead of the Will naming the beneficiaries, the State determines who receives the money. Spouse and children come first. Then grandchildren if Spouse and children are deceased. If no grands, siblings next, no sibs, then parents. No family at all then the state will take the estate. The money may have to be kept for a certain amt of years just in case a family member comes forward. Not sure if the administrator receives the same % of the estate as the Executor. So if not family, being an Administrator would be null and void.

The state takes over. The body may be unclaimed. It is provided burial by the state.