Yes people do fail the TR and yes they do fail the base training and yes you can fail line training.
Paying for a TR is no guarantee whatsoever of reaching the necessary standard. Just the same as if the airline was paying.
Ryanair set a very high standard that has to be achieved. It needs to know it's people are the right people as a hull loss resulting from poor pilot ability would be very very serious.
For the ground school you simply need to know your stuff and answer the questions. For the sim and beyond it is about ability to perform. You are given chances but if you need extra sim sessions then you pay for them, and they're not cheap. You can still get chopped. It's not unusual to hear of people failing the base (circuits) training but the company will put them back in the sim and give them another crack at it. They don't charge for that. It's in their interest at this stage to try and get you through.
When I did my TR in 2007 one person from my course was chopped and also someone on the course behind us. Both were down to lack of ability. Pure and simple. Plenty of chances were given. Remedial training was given. Do bear in mind that your sim buddy is having to accompany you through all this even though of course they don't pay for the training they don't need. You do.
I also know of someone who was chopped during line training (easyjet) who simply couldn't land with any sort of consistency. They were given a lot of sectors but to no avail.
There is no chance that a trainer will just chop you for no reason. You'll be thoroughly debriefed. Written records are kept and it's all discussed with both you are your sim buddy together. If there's any chance of you getting chopped you'll be only too well aware of why and that it's a possibility.
Once you're in to any airline the struggle is not over. You will have to work harder than you would believe to make the grade. It's not easy but it does get easier and of course one day you'll look back and wonder what all the fuss was about.
Get the job. Get your head down and enjoy it.