Most leases have a clause governing assignment and subletting. When you add or replace roommates you are subletting part of the unit, so the subletting cause in your lease applies.
If you’re a sub-tenant/not on the lease, what are your rights? Can the master tenant kick you out, or raise the rent, at his/her discretion?
The truly bad master tenant collects all of the roommates’ rent and then, for whatever reason, doesn’t pay the landlord. Usually you find out about the problem too late, when you’re being evicted.