Combining random samples from different seeds. Is it unbiased?

Let us draw s random samples uniformly at random. The code is using a pseudorandom generator. I do not fix the seed. Then I draw t more random samples using the same code but a new run. The seed is again not fixed.

Can I combine the samples and get an unbiased estimate? What if I fixed manually two different seeds? What if I fixed the same seed for both runs?