HI
Cats can be infected by a number of different species of tapeworm but the most common one to do is Dipylidium caninum. The eggs from this tapeworm are expelled in "packets" which are often seen sticking to the area surrounding the anus in cats. These egg packets can survive many months under the right conditions but that is not so relevant because in order to reinfect another host they must be ingested by a flea and that flea must then be eaten by the new host.The egg packets (proglottids) are usually either washed off by the cat or ingested by the flea quite quickly. Any that drop off into the environment are very unlikley to be eaten by a flea and so perish in time. I repeat that these proglottids in the environment (or on the host) cannot directly infect the same or another host.
I hope this answer has been helpful.
Kindest regards, Peter