The local authority would have a claim against any money in any accounts your mother maintains in her name and any other assets. If these combined sums total £23,350 or more (which presumably would be the case), the local authority has a claim against everything above that sum. Once your mothers capital reduces below £23,350, the local authority will begin contributing towards her care until her savings reach £14,250.
After the savings reduce below £23,500 they will expect your mother to contribute 1 pound for every £250 of capital she has between £14,250 and £23,350. They would also have a claim against any money she receives as income except for some minor amounts that he is allowed to keep for her own spending requirements. After her savings reach £14,250, the council will fully fund his care without contribution from him at all.
any property that is purchased with your mother's assets would remain liable to potential future claims from the local authority as may become necessary subject to the above maximum limits and accordingly, any property purchased would potentially be vulnerable to a future requirement to sell as needs dictate.
Remember however that there are potential financial solutions such as that referred to above which can give security and certainty in respect of your mother's finances and these are well worth exploring.
Does the above answer all your questions or is there anything I can clarify or help you with any further?