This is a classic scenario.
A timber floor joist has been in contact with a damp wall for a considerable period resulting in the onset of wet rot. The timber becomes “crumbly” and loses its structural integrity (strength). The floor the joist supports in turn becomes unsteady underfoot resulting in the need for part or full replacement of the joists.
It may be possible to repair them in one of a number of ways. To avoid such a problem in the first place do what you can to limit the contact between the timber and the source of damp. Wedging slate beneath the joist is a sensible and low cost option. Another alternative would be to suspend the joist from a “joist hanger”, the metal hanger being in contact with the damp wall rather than the timber itself.