You didn't describe how the lock was broken, so I can't comment on that.
However, as a 25+ year Cessna owner I can testify to the fact that the
doors are not very secure when closed in the usual manner. I have on a
number of occasions gone to the airport, found the door open, and nothing
missing. When the wind blows the fuselage twists a little, and the doors,
if not solidly latched, will pop open.

There are two things you can do about this. First, close the doors securely.
In a Cessna you can leve the handle pointing downwards - and the outside
release will work. Or you can turn it to the fully locked position (handle
pointing towards the rear) as you do before taking off. This causes the
latch to more deeply engage the hole in the striker plate. Watch what
happens when you operate the handle with the door open to see what I mean.
How to fully lock both doors? Lock the passenger side when you are in the
plane. Then get out and close the pilot's door. Open the baggage door and
stick your head and shoulders inside. Fold the rear seatback forward, then
reach for the pilot's door handle and rotate it to the rear position.
Extricate yourself from the plane, and lock the baggage door.

For added security. install an eyebolt in the lower rear corner of each door
(inside, of course). Then run a suitable bungee cord between the eyebolts
when you are closing up the plane.

I hope this helps - it works for me.