Should I sign an Undertaking

[Julius 2025]

Hi there. A fair few months ago my partner of 20+ years passed away - we were not married. I am the main beneficiary but that is our shared house - no mortgage.
The Executors of his estate (solicitors) are concerned that there isn't enough money to meet all outgoings.
This is only based on what I have provided, not a full administration of the Estate (I know he had life insurance but not how much for example).
Originally they wanted some money to inject funds, but I declined.
They now want me to sign an Undertaking that if there's a cash shortfall I will pay it, or if in the most extreme case it will give them permission to go ahead with the sale of the property.
They will also be 'more than happy to press on with the administration of the Estate' if I do so.
Simple question - should I sign?

[PallasAthena]

Is the Estate liable to IHT? If so is the issue that there isn't enough cash in the estate to pay the IHT bill?

Does the Will specifically state that the house is left to you or is it that the Will just leaves the residual estate to you but that most of the residual estate will be the house?

[atticus]

Has probate been applied for? If not, why not ask the solicitors to renounce the right to be executors and do that yourself as main beneficiary?

[Julius 2025]

Thank you for the replies. I don't think IHT will be an issue as the house that is left to me is with less than £500k. The will does state teat the house will be left t me.
I think they're concerned that there may not be enough money to pay for debts, including a small loan he took out (£7k).
As far as I understand no probate has been applied for as they haven't done anything except write to me asking for money.
I'm in my 70s but I guess I could ask them to renounce the right and do it myself.