This is a class 9/10 noun (N class) so it's singular or plural with no change to the noun itself, although other words in the sentence may show it.
Umemwona mende yangu? = Have you seen my cockroach?
Umewaona mende zangu? = Have you seen my cockroaches?
Tips section (animals lessons) says all animal nouns (although they might be from different classes) follow m-wa class agreements. So, why yangu/zangu and not wangu (m-wa)? Im missing something?
Because N class nouns are the same in singular and plural, and M/Wa possessive agreements are the same singular and plural. This means "my cockroach" and "my cockroaches" would both be mende wangu. Using the N-class possessive (and only the possessive, the rest follows M/Wa rules) helps differentiate between the two.
Correction:- as I now understand it, this rule only applies to a group of nouns for people in class 9/10 which talk about relations:
baba, mama, ndugu, dada, kaka, babu, bibi, nyanya, rafiki, adui etc.
It can also apply to animals, particularly in plural, eg.:
ng'ombe wangu = my cow
zangu = my cows
... but I think that's kind of old usage, so both sentences I wrote above would probably have wangu.