Yeast Health

I am a little confused about the health of yeast produced in starters where the viability (health) of the yeast used to produce the starter is less than ideal.

For example lets say I have rinsed yeast stored under water in a fridge for 12 months and I reactivate them in starters. Will the new yeast created be healthy or bunch of weaklings that will produce off flavors in my brew?

Is there any issue with the dead yeast in the starter being mixed with the new yeast and put into the wort or will they just provide nutrient for the living yeast cells?

The number of dead yeast cells will be minimal compared to the final batch size, so you should have no issue with them. The new yeast may be ever so slightly different than the original strain, but I don't think you will notice a difference.