Can I check if a Mirror database was synchronized when the principal died? having 2 machines, one being the principal and the second one as a mirror in case of failure of the 1st one. without witness but in High Safety mode
Is any way to check if the mirror DB was synchronised when the Principal has failed?
I need this because I'm concerned if:

1-the mirror goes down
2-the Principal does a lot of work (while mirror is down)
3-the mirror come up, and starts synchronising, while synchronizing the principal goes down

in this situation, can I detect the mirror is not up to date without a witness??
So...is there a way to check if the Mirror database is up to date while the Principal is down?
Edit:
I tried to use a Event Notification, to keep track of mirroring changes, but theses notifications are asynchronous, so there is a gap I cant cover.
Is any other way?
You can check the mirroring_state_desc in sys.database_mirroring.  It will tell you if the databases are in sync, this does depend on if you're running in High Safety or High Performance mode.  In High Performance mode as long as the mirroring process is running it will show state of SYNCHRONIZED while the actual state of the database can be behind as the log records are still being applied.

In this disaster type scenario, I believe the mirroring would be broken and it would be best to know the various ways to get a tail of the log backup combined with the normal course of database and transaction log backups to restore to the point of failure.

Tables 5-7 in this TechNet article cover the various scenarios against the statues reported.