No you cannot. Normally, you would place the card in your Buddy Zone on the field, and the other card in your Buddy Zone at [Rest]. However, since your Buddy is deleted, and flipped face down, it loses its name, so you cannot Buddy Call.
What happens if I try to delete a Buddy that is already flipped face down?
Nothing will happen, since the Buddy is already flipped face down.
On a related note, your opponent can still flip his or her Buddy face up after using "Belost".
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