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We say varieties sit in a family, if there is a flat family over a (irreducible or connected) variety of finite type, such that these varieties appear as fibers of this flat family.
As the above post said, the negative &-\kappa& case is implied by the effective Iitaka fibration conjecture， which I think is expected to be true but still widely open in general.
I'm a bit confused. In the second example you give, is it also a smoothing by itself as the quotient will identify $f_t$ and $f_{-t}$ as one smooth fiber for $t\neq 0$?
