A few months ago, I decided to quit my job, resulting in 3 months notice, reduced to 1,5 months through negotiation. Things were going quite terribly as I was completely unmotivated by the work I was assigned. I kept reading my mail, answering it and working, though very slowly and not very well, but what you could call my manager started sending mail to me (with mostly negative content regarding my motivation) on my personal address. At the time, I had already found a new job and was only focused on hanging until the end of my notice, so I could leave and never look back. I did not answer the mail received on my personal inbox, nor did I mentioned anything to anyone about it as their content was professional and not insulting or inappropriate, and I think it was the correct decision in that particular situation.
I was wondering : what would have been the right course of action if I was not close to leaving the company ? I could let it go because I only had a few weeks left, but what if I hadn't quit, and she kept emailing me on my personal address on a regular basis ?
It is a small company, so no HR.