When a person dies the immediate concern of his heir or the executor of his estate is to determine whether he left sufficient property to pay his debts and legacies.
In England, after the days of William the Conqueror, this was known by the Anglo-French legal term, aver assetz, from aver, to have, and assetz, sufficient, hence “to have sufficient (to meet the claims).”
In the French of today this would be avoir asset.
Thus assets, stripped of meanings that it has acquired through the years, rightfully means nothing more than “sufficient.”