Fixing a broken pipe underground without breaking the floor
The answer to your question is "yes" - but it's a specialist job.  For example http://insitudrain.co.uk/commercial-industrial-services/cure-lining/ can remotely apply a liner and then cure it. (I found them by searching for "in-situ drain repair".

If you are contemplating a DIY approach, it's probably easier to dig down, repair, and make good.