A version constraint without an upper bound such as *, >=3.4 or
dev-master will allow updates to any future version of the dependency.
This includes major versions breaking backward compatibility.
Once a release of your package is tagged, you cannot tweak its dependencies anymore in case a dependency breaks BC - you have to do a new release but the previous one stays broken.
The only good alternative is to define an upper bound on your constraints, which you can increase in a new release after testing that your package is compatible with the new major version of your dependency.
For example instead of using >=3.4 you should use ~3.4 which allows all
versions up to 3.999 but does not include 4.0 and above. The ^ operator
works very well with libraries following semantic versioning.
Note: As a package maintainer, you can make the life of your users easier by providing an alias version for your development branch to allow it to match bound constraints.