First of all, no airline is going to risk letting passengers back on board a plane after an emergency exit - that would be a huge liability risk for them.
With that said, a quick google found:
What happens to passengers’ belongings when left in an aircraft after an emergency evacuation?
Typically, the luggage will remain on the aircraft until they can be
safely retrieved. If the emergency landing takes place at an airport,
the belongings would be taken from the aircraft and transported to the
terminal where they will be made available to passengers as soon as
Airlines will make every effort to contact passengers and inform them
about the recovery of their belongings. Contact details provided
during the booking or check-in process are used to reach out to
passengers. They are then instructed on how and where to retrieve
And also this forum which talks about the legal responsibilities:
49 CFR 830.10 - Preservation of aircraft wreckage, mail, cargo, and
§ 830.10 Preservation of aircraft wreckage, mail, cargo, and records.
(a) The operator of an aircraft involved in an accident or incident
for which notification must be given is responsible for preserving to
the extent possible any aircraft wreckage, cargo, and mail aboard the
aircraft, and all records, including all recording mediums of flight,
maintenance, and voice recorders, pertaining to the operation and
maintenance of the aircraft and to the airmen until the Board takes
custody thereof or a release is granted pursuant to § 831.12(b) of
(b) Prior to the time the Board or its authorized representative takes
custody of aircraft wreckage, mail, or cargo, such wreckage, mail, or
cargo may not be disturbed or moved except to the extent necessary:
(1) To remove persons injured or trapped;
(2) To protect the wreckage from further damage; or
(3) To protect the public from injury.
(c) Where it is necessary to move aircraft wreckage, mail or cargo,
sketches, descriptive notes, and photographs shall be made, if
possible, of the original positions and condition of the wreckage and
any significant impact marks.
(d) The operator of an aircraft involved in an accident or incident
shall retain all records, reports, internal documents, and memoranda
dealing with the accident or incident, until authorized by the Board
to the contrary.
As for your specific scenarios:
The checked baggage should be considered disposable, and the airline will provide what ever is needed by the passenger in the short term (this would also the same scenario as if the baggage was lost in transit)
The insulin dependent passenger should inform the airline, which would lead to consultation with a medical practitioner.
Sorry, but the dog is SOL until the airline is able to retrieve it.