As far as I am aware, a proxy is just a server that you can connect to, to access the www (or whatever else). It is simply a server with an IP like any other server.
Some are listed for public use. In which case they may be 'detectable' because they have agreed to be on someone's 'list' of proxies. (As far as I can see these lists are useless because often, users hosts will change their IP.)
I could start a proxy now on my home pc, but it would be useless to you if you wanted to use it after I switched it off when I went to bed.
Of course, I could be totally wrong; if so, someone please correct me.