Must an FDW go home when her work permit expires?

Normally yes, but not if her employer agrees to employ her for two more years and gets her work permit extended for another term.

If her employer does not wish to renew the employment contract, the FDW will not need to go home if she finds alternative employment and a new work permit is issued to her to work for her new employer.

If the FDW is transferred, the old employer would be advised in due course, by Immigration, that his liability under the Security Bond is discharged.