Short answer. Yes. Article 389 of the Civil Code provides that administration ceases when a third person appears, showing by a proper document that he has acquired the absentee's property by purchase or other title. Once that happens, the administrator stops performing that office and the property goes to whoever has the right to it.
What the law says
When a third person appears, showing by a proper document that he has acquired the absentee's property by purchase or other title
Civil Code, Article 389 — When Administration Ceases. Read the full provision →
What the law says
In these cases the administrator shall cease in the performance of his office, and the property shall be at the disposal of those who may have a right thereto
Civil Code, Article 389 — When Administration Ceases. Read the full provision →
What Article 389 lists as grounds for ending administration
Article 389 of the Civil Code lists three specific situations that end an absentee's administration: "(1) When the absentee appears personally or by means of an agent; (2) When the death of the absentee is proved and his testate or intestate heirs appear; (3) When a third person appears, showing by a proper document that he has acquired the absentee's property by purchase or other title." A lawful buyer coming forward is the third of these named grounds.
The specific ground for a lawful purchase
The third ground answers your question directly: "When a third person appears, showing by a proper document that he has acquired the absentee's property by purchase or other title." If someone can actually show a proper document establishing that they acquired the property by purchase — or by some other title — that appearance is, by itself, one of the events Article 389 treats as ending the administration.
What has to actually be shown
The text requires more than a bare claim of purchase — it requires being shown "by a proper document." The article does not itself define exactly what makes a document "proper" for this purpose, but the emphasis on documentary proof means the buyer's word alone, without something to substantiate the acquisition, would not be what this specific ground describes. What counts as adequate proof in a particular case is a factual question the article leaves to be worked out on the actual evidence presented.
What happens once administration ends
Article 389 also states the consequence that follows any of the three grounds: "In these cases the administrator shall cease in the performance of his office, and the property shall be at the disposal of those who may have a right thereto." Once a proper document establishes the purchase, the administrator's role over that property comes to an end, and the property becomes available to whoever actually has the right to it — which, on the facts you describe, would be the buyer who acquired it.