Hi @Catlover19 , Savings/capital of £6k or less are ignored by UC. If your savings are currently £10K, they will reduce UC but you may still receive UC, just a lower amount (for each £250 you have above £6,000, your UC is reduced by £4.35).
If your savings are now over £16K, that will mean you're generally not currently entitled to UC and you won't be entitled for however long your savings are above £16k (capital limit is £16K). But you can sometimes have savings over £16K for 6 months (sometimes longer) and get UC through a 'capital disregard'- eg if you've just sold your home and the money is in the bank while you sort the purchase of a new home.
UC has some rules about not being allowed to deliberately deprive yourself of capital in order to get more UC, but you are allowed to spend savings to reduce debt (including mortgage debt). See H1796 (pg 64) in the UC guidance Advice for Decision Makers Chapter H1: Capital (google it).
If you're going to give the £10K to your ex to buy him out, I'm not sure if UC would see that as paying a 'debt'. Might be a good idea to see a benefits advisor in that situation.
(Using savings/capital to purchase 'goods and services' can be tricky because a UC decision maker may decide the purchase is not 'reasonable' so if you were planning on spending a big chunk of money on eg updating your furniture, again, you might want to get advice first!)