Not dogs or cats but gifts between individuals which in lifetime are potentially exempt transfers (PETS).
Should the donor survive more than seven years from the date of the gift, the value of the gift drops out of the estate.
Should the donor die before reaching the 7 year anniversary of the date of the gift, any inheritance tax found to be payable is usually borne by the donee. This is a particular issue if the value of the assets has gone down.
Fortunately relief is at hand. An election can be made within 4 years of the date of the death of the donor to elect to substitute current market value. This also applies if the asset has been sold for less than the value of the gift.
Alternatively, or as well as, one could take out term life insurance to cover the potential liability.