How do phages die after killing bacteria? What happens to phages after they die?

Answer 1

If you're referring to a bacteriophage, these are a form of virus, which are not technically alive and thus cannot die.

Phages will simply remain until they deteriorate under environmental conditions, or until they infect a new bacterium and replicate.

The initial virion infecting a cell will attach to a bacterial surface and inject its genetic material. After doing so, the remaining capsid structure is inert - it will simply remain or deteriorate under environmental conditions.