Those usually show for MMS, so they would have to make sure that they have a valid mobile data connection (MMS only works through WiFi IF the device/carrier supports WiFi calling or they're using a carrier app with WiFi support, like Verizon's Messages+ or T-Mobile's DIGITS app).
They should also check their settings to see if roaming restrictions aren't kicking in (i.e. mobile data while roaming or, depending on the messaging app, MMS auto-download while roaming).
I've had several issues getting MMS properly even through WiFi calling when traveling abroad, for instance, and would get a barrage of them once I landed in US territory.