Three days after we got our puppy we saw a hawk on our back fence, so she's never really outside unsupervised for very long. I'll go out with her, then maybe let her stay out a few minutes while I run in, but only after I make sure the sky is clear.
Our girl doesn't dig much, but I've heard some dachshunds can get under a fence pretty quick, so having them outside without you there isn't such a good idea anyway.