It will depend on a few things, but mostly the relationship the other directors/owners have with the bank and how profitable the company is.
Depending on its cash reserves taking out 500k could cause issues with the bank and suppliers (even if it is replaced as a loan as that will show up as a short term liability).
Banks generally are not keen to advance more than 250k backed by personal guarantees or take houses etc. these days or as an OD so they may need to look at a diffent way to buy him out - maybe a staged buy back over a number of years as the company can afford it.
Need to clear if they are expecting her to get a loan and inject personal money or the business to borrow it to buy him out and they are appointing her as a partner at the same time.
Are they partners or is it an ltd as rules are quite different for partnerships as all partners are liable for the business' debts and so a staged buy back may be much harder to arrange ?