I came across this when I went into hospital 8 months into an annual.
The refund wasn't enough to cover the couple of months remaining

you "only" pay for 40 weeks, so you effectively get 3 months "free"

Understood - but it was refund or nothing - I asked for 6 weeks on the end
of the ticket. It's only a bit of paper and I wouldn't have gained out of
it. I never did renew after that and am now driving instead.

Or, to look at it another way, you're getting a discount of about 23%

TfL don't see the annual as discounted - it's an allowance for leave and
sickness. They also said when you buy an annual it's an undertaking to
travel for at least twelve months.

Cheers,
Dave