Two days ago, I accepted a desired faculty job offer and cancelled an on-campus interview at another university that was scheduled for three days later. I wanted to be honest and not waste their time. However, the university has asked me to pay for the flight ticket they purchased for me due to the cancellation. Is this normal? Any suggestions would be greatly appreciated.
Actually I don’t think it’s right of them. If you had gone to the second interview you would have wasted everybody’s time in addition to hotel and meal expenses for your stay at the second place.
Part of the cost of advertising a position is that some candidates will change their minds at the last minute, or will have to reschedule because of some unforeseen event. I can understand the 2nd institution not being happy about you cancelling but you did the right thing by telling them ahead of time that you would not accept their offer. Moreover, it’s usually possible to get a travel credit even on non-refundable tickets so the cancelled fare is not an entire loss.
When any potential employer offers to pay for any of a job candidate's interview expenses, they accept the risk that the candidate won't accept the offer. Suppose you had gone to the interview and then declined to take the job. It's very unlikely that they would have asked you to refund your plane ticket. You're simply reducing the time delay between the time when they buy your ticket and the time when they learn that you won't be accepting the job.
In the highly unlikely scenario that they would have asked you to refund your plane ticket even if you had done the full interview process and then declined the offer, then they're being consistent in asking you to refund it in this situation. But that would be such a significant departure from the usual norms of job interviews that the onus would be on them to clearly convey that fact before they bought your plane ticket, and to then ask you whether you still wanted them to buy your ticket, knowing that you would be expected to refund it if you later declined their offer.
I think you should politely decline to refund the ticket.
Edit: After writing that answer, I came across two near-duplicates at Travel reimbursement for interview after accepting another position and Interview not reimbursed if offer is made but not accepted (UK). The answers to those questions seem to indicate that it is more common than I had previously understood to decline to reimburse interview expenses if the candidate declines the job offer, especially in the UK. So I am now a little less categorical in my answer. I still think that the university's reimbursement policy should be the same whether or not the person actually attends the interview, but now I guess it's more of an edge case as to whether it's reasonable for the university to decline to cover the travel expenses in either case. Either way, the university should have clearly conveyed to the candidate before buying their ticket that the candidate would be on the hook for travel expenses if they ended up declining the job offer.
Certainly it is fair. The choice was yours. It wouldn't be fair if they had cancelled. They made the purchase in good faith in this situation with little opportunity to avoid it.
I suspect it is pretty normal, though maybe not universal.
What I think is more common, perhaps for exactly this reason, is to ask the candidate to make their own arrangements for travel and to promise reimbursement after the visit. Many object to that policy, I think.
And, an alternative you had, but didn't exercise (or think of, probably) is to tell them you were very unlikely to accept any offer and ask if you should still come. If they had said no, then you'd have a case that they should just absorb the cost.
I don't know, actually, whether you are bound to reimburse them. They might actually let you off the hook if you just say you are sorry, but are unable to provide the funds.