Just a silly question, but if you were in a leasehold property, had a mortgage, say take out 60 years ago, and the lease runs out next year, your mortgage paid up 20 odd years ago, what happens? are you thrown out, do you have any rights? is the house you paid for not yours any longer? why do people have leases on property?
You don't leave it that late before you buy a new lease. It would cost too much. You need to renew I would sat by at least when you have 50 years remaining. Except central London which is a law unto itself where a 25 year lease can be considered good.
I bought a flat with a 99 year lease which would have seen me out - but I moved a couple of years later. You negotiate with the leaseholder for a new lease, in good time.
I'm no legal eagle but my understanding is that you still own the house, but own no land upon which to move it. Consequently renewing or buying the leasehold for the land upon which it already stands becomes very valuable to you by that stage. Never let it get that far and think about having to sell up in 20 odd years time when you are thinking of buying a leashold property now.
You own nothing when the lease expires. LH is just renting with certain rights which expire when the lease expires. You should renegitiate the lease when it get's to a level beyond which you cannot get a mortgage. That varies of course but most lenders would require a 70years remaining at least. These days Leases are often sold with 999year terms.