I sound like I'm selling eBay, but I'm not. I actually really dislike what eBay has decided to become, but it is what it is, so...
Just an example though:
Today is nothing special, and there are a couple desoldering base stations which have no hand pieces, selling for under $20.
There are a couple hand pieces currently for under $20. This isn't as common on eBay, but there are at least three today.
The hand pieces may (probably?) need heating elements replaced, but maybe not. These are about $20.
So today is just another day, and a guy could get one together for about $80 including shipping. On a good day this can come down much more.
My rig was a Hakko 703B soldering/desoldering station. I picked up the base station for dirt cheap off eBay thinking it would be easy to get replacement handpieces. It wasn't as easy as I thought, but I eventually bought two soldering and one desoldering handpiece and some tips from SRA. They weren't compatible with the Hakko base station so I bought heating elements for each directly from Hakko and they were a screw-right-in fit with the SRA handles. I had to replace the connector plugs too, which were standard DIN plugs. Some reassembly and I was in business. If I could have been more patient and found actual Hakko handpieces on eBay it would have been easier and probably cheaper. All together my grand total was less than $150 for an extremely nice rework station and it could have been cheaper. I never need two different soldering irons with my limited knowledge and with what I do, but I guess now I have a spare in case it goes south someday, or if I ever do need two they are there.
Pace stuff is supposed to be really nice too and that brand is often found on eBay.