Both parents have been declared unfit (drugs), the 7 yr old is with the grandmother who is visited by child protective services, the state (MISSOURI) totally supports the grandmother. The question is:

When can the grandmother seek full custody which she needs for legal reasons

Or does she need full custody?

Can the state of Missouri declare the child abandoned after a period (what is time limit to leave a child)?

Grandmother not receiving any state help (assistance) in supporting child, is there any help available?

First, there is no need to declare the child abandoned. CPS has the right to remove a child from parents they deem unfit. Grandma should first ask for temporary guardianship so she can legally provide care for the child. This will include getting public assistance. The CPS caseworker should be able to advise what is available and help apply.

Eventually, gramdma can apply for full permanent custody.