Hi majw20,
We understand that you're running into some trouble with the Emergency Bypass option in contact cards, and we're here to help. To clarify, you should still see the option for Emergency Bypass if you open the contact card, and then tap Edit > Ringtone (or Text Tone) > Emergency Bypass. Is this not happening? Also, are you currently using custom tones for the contacts experiencing the problem? The reason we ask is that any tones our sounds being used must be downloaded to the iPhone, otherwise they may not work, as the iPhone isn't able to stream audio for notifications. We have more information in Change message notifications on iPhone
If this behavior is only happening with a certain set of contacts, please let us know those details as well.
We look forward to hearing back from you soon. Take care!