ESA letter from jobcenter plus ???

At the start of my wife's illness she claimed (at the DWP's advice and help!) ESA as she had paid NI contributions. Not 100% sure now as it was so long ago , the payments stopped and was transferred to PIP ( again at the DWP's advice and help!)
Strange thing is we keep getting letters from the job center every year since telling us they cannot pay the ESA!
No big deal really as she not eligable for it but should we just let them know she's not trying to claim ESA to stop the yearly letters of just leave it ?
On that score i was wondering if anyone else was getting this sort of 'random' mail?

thanks for your reply which makes sense.
I realise ESA and PIP are separate benefits, was just confused as to why they keep sending letters.

As for when I say 'transferred' I should have said one claim closed and another different one opened. This happened many years ago but as I said, keep getting the ESA letters which when at first arrive cause some worry if that makes sense