Existence in logic vs existence in reality

Take an object which has been destroyed, we can talk about it in the past tense, how does this work logically, can we talk about objects which previously existed (in the physical sense)? For the object to be discussed it must be an object in our language, and therefore if we have a constant symbol 'y' for this object, the statement

∃x(x=y) i.e there exists an object x that is y (the object that does not exist physically)

Is the existence implied by the existential quantifier different then our 'physical' definition or do we need to adjust our definition based on the domain, i.e if we can talk about it, it is in the domain and 'exists' logically?

However, anything we say about it is limited to past tense in natural language, would all possible predicates be based on functions that map in the past tense? For example:

'The dodo was a breed of bird'

Logically let D denote The Dodo

P(D) must be 'D was a breed of bird' and not 'D is a breed of bird' as P(D) would be false if it denoted the latter.

How do we differ with the use of 'existence'?