Is it possible to install Photoshop 2015 on a free membership plan after having previos access
What do you mean by a free membership plan? Perpetual licences have been retired. It's subscription only now I'm afriad.
The Photography Plan includes the latest version of Photoshop and updates as they become available plus Lightroom and some cloud storage for about $10 a month.
If your question is "I used to subscribe but now I don't subscribe - can I run the old app for free" - the answer is no.
If your question is "Can I run old versions while on a free trial"- the answer is no.
If your question is "I would get a paid membership if I could run Photoshop 2015" the answer is "Photoshop 2015 is not available any more, not even for money".
Old versions may run on a machine for 7 days as a free trial after that 7 days the Photoshop will not longer function and can not be re install as a trial the trial on that machine is over. There is no Free Photoshop from Adobe.