How does the nature of space-time and how we are able to interact within it relate to the expansion of space? If Space expansion ceased to be a constant would a body of mass still be able to change it's positional distance in relation to the location of other bodies of mass? And, if mass could still move thru space-time, would there be any theoretically posed effects of considerable difference caused as a result of mass traveling faster than expanding space-time since, really any traversing speed that an object could pose would exceed the halted to a stop, expansion of space-time?
Time is the aging of a clock (in a large sense, massive particles may also be considered as such clocks). The encounter of two particles is called an event which depends on the coordinate time of the concerned particles, that means it depends on two clocks.
Space expansion is described by the Hubble constant which has the unit 1/sec. That means that space is expanding each second by a certain percentage. That means that space expansion itself is a clock.
Conclusion: Even if one clock (i.e. space expansion) would not be working, the others will continue to exist.