Legal Question in Real Estate Law in California

CAN they? Anyone CAN do anything they like. Whether you have an enforceable written contract with the lender will determine if you have an grounds for a breach claim against them. Unless you can informally resolve this with the lender and get funded, you will lose the purchase deal because of your breach. Thereafter, you can spend time and money filing suit against the lender if there are grounds for it. If serious about getting legal help in this, feel free to contact me.

You are not clear on what documents were signed. If you are the seller and the purchaser's loan was not approved, then the question would arise as to whether your sale was contingent on the purchaser obtaining financing. If it was, then the failure to get the loan would be a failure of a contingency and not a breach of contract.