Minimum supported rust version (MSRV) policy that indicates the most recent stable rust release is the minimum whenever a new crate version is published. It is not required to bump a crate's major version after a new stable compiler is released.
For example crate_foo version 0.1.2 published on 2018-12-28 has MSRV 1.31.1 as this compiler was published on 2018-12-20.
The advantages of this approach is simplicity in maintaining a crate's code.
If you are unable to update your compiler, you may be unable to update crate dependencies following this policy.
Dependencies can be pinned to a version as old as your compiler, e.g. =0.1.2. Lockfiles may be updated with cargo update -p crate_foo --precise 0.1.2 where version 0.1.2 is old enough to ensure compatibility.
Hopefully better tools to deal with MSRV will become available, as there is not general agreement about how handle this issue currently.