In the United States one would file a petition with the appropriate court to have a conservator appointed for the individual. I suspect that you are probably asking about U.K. law since you mention a "solicitor", although a few other countries also use that term.
The process is essentially the same everywhere in the common law world, although the terminology may be slightly different from place to place.
If the court finds that the person isn't competent to manage their property, then it appoints someone to do that for what we call where I practice the "protected person" and that person has to account to the court and interested family members about how that is being done on a periodic basis.
If the court finds that the person is sufficiently competent to manage their property, then it declines to appoint a conservator, and the people who brought the petition that was denied probably end up eating the legal fees that they incurred to do so.
Usually, the decision of the judge is based upon one or more reports from health care and financial professionals and some testimony from ordinary people about the behavior that they have observed and testimony from the person to be protected if that person contests that appointment.
If the issue goes beyond financial management to self-care issues, then one files a petition to have a guardian and conservator (who could be two different people or the same person), in whatever terminology is used in the U.K. for those posts, to be appointed. A conservator only has authority over someone's significant property, a guardian has more hands on parental-type authority to physically regulate how that person lives their life (e.g. the authority to insist that they go to a doctor and get prescriptions to treat their condition).
Petitions to have a court appoint a guardian and/or conservator that are granted usually have the legal work paid for out of the protected person's assets, although the initial funds to hire the solicitor would come from the interested family member's funds.
If the facts are obvious and the case is not disputed by the protected person or anyone else (e.g. there could be no doubt that a conservator is needed but relatives could fight over who should be appointed to that job), then a case like this is not all that expensive - probably $3,000 to $12,000 in the U.S. for lawyers and experts. In a contested case, the litigation costs and the amount of time it takes to resolve the question of whether someone should be appointed permanently as a conservator can easily be ten times a great as that, and more in cases where there are high stakes and bitter family disputes being worked through in the court system.
A trust is not likely to be an option in a case like this one.
While, in practice, a trust is similar to a conservatorship, in the case of a trust, someone who is competent at the time and has money and/or property puts it in a trust, with pre-established rules for its management that the person establishing the trust (called a grantor or settlor or trustor in most cases) defines, names a trustee and usually sets up rules for filling vacancies in the trusteeship. Sometimes people create trusts for the benefit of someone else, less often, people create trusts for the benefit of their future selves.
But, you can't create a trust if you are already incompetent, which the OP seems to suggest that this person already is for all relevant purposes.
