This is the 1961st most frequent Russian word.
собственную
"Own" (possessive, feminine singular accusative form).
Here, 'собственную' is used as an adjective in the accusative case to indicate that the clinic belongs specifically to her, highlighting personal ownership.
Она построила собственную клинику.
She built her own clinic.
In this sentence, 'собственную' modifies 'проблему,' also in the accusative case, and signifies that the problem is personal to him.
Ему пришлось решить собственную проблему.
He had to solve his own problem.
'Собственной' here is in the prepositional case, describing the safety that is specific to themselves, used to emphasize individual responsibility or concern.