>> Can I be sure they won't be shut down and thereby leave me cut of from all my online services?
> Yes, if it syncs to something like Dropbox that has a local copy.
This isn't necessarily true. If Dropbox was legally coerced to do so, they have the technical means to erase any file in your Dropbox from each machine as it connects to the network. I believe they already do a best-effort version of this if someone stops sharing a folder with you. All it would take is a court order to remove a file and all its backups from Dropbox's server, which might happen without even targeting you specifically because Dropbox does deduplication and doesn't encrypt your data.
This may be very unlikely, especially with an encrypted password database unique to you, but it's not impossible. At least we can presume that a general takedown or Dropbox becoming unavailable for whatever reason won't cause this to happen.
> Yes, if it syncs to something like Dropbox that has a local copy.
This isn't necessarily true. If Dropbox was legally coerced to do so, they have the technical means to erase any file in your Dropbox from each machine as it connects to the network. I believe they already do a best-effort version of this if someone stops sharing a folder with you. All it would take is a court order to remove a file and all its backups from Dropbox's server, which might happen without even targeting you specifically because Dropbox does deduplication and doesn't encrypt your data.
This may be very unlikely, especially with an encrypted password database unique to you, but it's not impossible. At least we can presume that a general takedown or Dropbox becoming unavailable for whatever reason won't cause this to happen.