The only noun I'd consider appropriate here is doormat, in the modern metaphorical usage:

doormat [noun]

...

[2] a submissive person who allows others to dominate them.

• to put up with such treatment you must be either a saint or a doormat_

[ODE; courtesy of Google.]

Other synonyms, like patsy and pushover, feel also too dated and/or too hypernymic.

The only noun I'd consider appropriate here is doormat, in the metaphorical usage, which 'feels' less dated† to me:

doormat [noun]

...

[2] a submissive person who allows others to dominate them.

• to put up with such treatment you must be either a saint or a doormat_

[ODE; courtesy of Google.]

Other synonyms, like 'patsy' and 'pushover', feel also too dated and/or too hypernymic. Though 'doormat' in the metaphorical usage cannot itself claim to be modern†; The Online Etymology Dictionary has it dating from at the latest 1861.