This is how I first got in to it. Was working for a company that sub contracted me out to another company. I started contracted for that company directly (while I was looking for another contract as I knew I was covering until the found someone). I doubled my salary then.
I'm fortunate in one respect as, if I am off long term sick my agency pays me 80% pay for 3yrs

Which is pretty sweet I have to say. They also put in to a pension pot for me (they have to by Swiss Law) as do I, which I can take as 50% lump sum when I leave (used to be 100% lump but people would take it and spend it instantly, so Swiss changed it) and take the rest at pension time. I did have to move from the UK to Switzerland though, as did my partner and 2 boys, so it's a massive uproot for everyone. I also have it quite lucky that although I'm qualified to do my job, they're always looking at new tech etc. which means I learn (which was a downside in going contract, lack of learning) and they're willing to train me as well if they get more out of me. Which is great.
So many people told me I was stupid for "taking the risk" but why? If it didn't work out, I'd come back, or go somewhere else. No perm job is actually permanent anyway. Roll the dice.