Selling:Puchaser/agent want tenant in before settlement

Unbeknown to me, agent was showing prospective tenants through my vacant property post sale. First I knew was when they rang to advise tenant had been found, and they want lease to begin 2 weeks before settlement date. Agent said "this is very normal, happens all the time". I was worried re my legal position if anything goes wrong re the tenants (ie damage, issues that need fixing etc before settlement. Purchaser said in email he would cover this but my conveyances says this has no legal weight and I would be liable.
Q1. Is there any way for purchaser to take on this liability before settlement , ie via licence agreement? Agent says yes, my conveyancer said no.
2. Tenants are ready to move in (!) and agent says "we're" all going to liable for their incurred costs if they can't move in on the date, despite me not having been party to this whole arrangement and finding out after fact. Any idea if this is correct? Seems impossible that I could be liable.
Thanks for your help.
1. Best to seek & follow the advice of your solicitor/conveyancer.
2. Ask the agent for a copy of the signed agreement where you gave them authority to lease the property. Sounds like they're working for the purchaser.
Does the contract give the purchaser the authority to look for tenants before settlement?
Does the contract permit the signing of tenants before settlement?
Get a lawyer!

What does your contract with the buyer say? Did you agree to allow early possession? If so under what terms?

What benefit do you gain in allowing this to happen?

Does your authority to the agent allow them to bring tenants through? I would imagine not.

Who will be the contracting party with the tenant? What about damage to the property?

Did you agree to provide vacant possession? Will it be vacant with their tenant in it?

It is not usual. I have never heard about this happening before.
Thank you all for your helpful replies and advice. The contract did not forsee this situation to my knowledge (am checking). The purchaser's lawyer has drawn up a "LIcence Agreement" which my conveyancer (who's not a lawyer) says can't overide the purchase of sale - ie that I remain owner until settlement. So I've said no to the tenants moving in. Don't know who's going to be up for their costs of removalists etc to be cancelled..
Sounds like a good outcome for you. As for costs for the new tenant, that isn't your problem :)

When I was selling I was about to arrange removal of the hired furniture when the agent said I'm paying for it so no need to get rid of it early. Turns out he wanted to keep it in to make it easier for him to find a tenant. I wasn't asked if prospective tenants could be shown through prior to settlement. There's more money in property management than sales so its obvious where the agents priorities lie.
I know if I asked my lawyer she would look at this and ask me if I was stark raving mad...

Move the settlement forward 2 weeks, see if the buyer can jump thru this hoop, otherwise why on earth would you take the risk.