You don't say how many miles this car has done nor how often it's been serviced, nor where serviced.
IF it's been serviced to the "book" by Jag dealers, you might get some goodwill as it isn't too far out of its warranty.

The only option a dealer can offer is a brand new engine. However, if you go to an independent garage they should be able to offer either a rebuild of the original motor or an exchange remanufactured unit, both of which would be much better value options. this could well be cheaper than a new engine even if Jag do contribute.

Part of the problem with any secondhand car is that you cannot know how it has been treated by any previous owner(s). And these days you cannot implicitly trust service stamps. For this reason whenever I buy a car I give it a thorough service, no matter what the records say. And then treat the car to regular oil changes (something hotly debated on here ad infinitum).

i can't help wondering why the injectors were changed if it's a big end failure???
If I were your friend I'd pay for their diagnosis but not the injectors (demand the old ones back) and recover the car (unless Jag are willing to help you out).

ATEOTD these things happen - it's the way the cookie crumbles!

Google 'jaguar XF problems', or google 'truedelta' reliability, compare jaguar with audi, and weep.

[I have just bought an 8yr old A8 and will be very unlucky if I have expensive bills - and I have no intention of changing the oil if I haven't done 10,000m in 365 days]