Assuming that the plan is subject to the Section 125 qualifying event rules (by virtue of employees being able to pay their premiums on a pre-tax basis), an employee or dependent simply moving would not allow the employee to make a mid-year change to their coverage. As background, Section 125 requires that employees be able to elect their coverage annually, and their elections cannot be changed mid-year without a qualifying event.
While there is a change in status qualifying event that includes a change in residence, that qualifying event is only permissible when that change in residence affects the participant’s or dependent’s eligibility for coverage. So unless the relocation makes the moving individual ineligible or newly eligible under the plan, the move would not be considered a change in status qualifying event.
On the other hand, there would likely be a qualifying event if the relocation resulted in the employee or dependent moving outside of a network that would provide service (for example if the plan were an HMO and the employee or dependent moved out of the HMO service area and therefore couldn't receive any coverage where they lived).
But if the employee or dependent is eligible under the plan before and after the move (which is often the case for PPO or HDHP plans with a national network), then change in residence is not a qualifying event. As such, the employer could not allow the employee to change their election mid-year absent some other qualifying event (like a marriage, birth, or divorce). Doing so would risk the disqualification of the entire plan (meaning that neither the employer nor employees could pay for their coverage on a pre-tax basis).
Now, there could be other qualifying events that would apply given the circumstances. For example, a cafeteria plan may permit a qualifying event for a loss of coverage under any group health coverage sponsored by a governmental or educational institution, including a foreign government group health plan. So if the relocating dependent has coverage through their government and will lose it by virtue of moving to the US, then that could make the move a qualifying event.
Keep in mind, though, that both the change in status and loss of coverage under a governmental health plan are permissible qualifying events, meaning that the plan document has to allow for them. Additionally, these events do not apply to health FSAs, so the employee could not change their health FSA election on account of either of those qualifying events.