In practice, its supposed to be earthed at the switch. A shielded cable should have a shielded RJ45 connector that crimps onto the shield and may also have an extra drain wire you can crimp onto the outside.
If you check the specification either for a
Registered
Jack
45 (literally a specific sized US telephony socket and nothing to do with Ethernet) or for an 8P8C socket and plug pair (which is
not RJ45), there is no definition of a screening point connection.
When a building is equipped with structured Ethernet cabling, that cabling (solid core cable) can be screened / earthed. By definition, that structured Ethernet cabling is from a socket to a socket. The normal earthing point would be at the patch panel end, where all of the individual drain-wires are connected to a dedicated low-impedance earth point (and not the building's mains supply earth). Individual, flexible, patch cables (i.e. plug to plug), used to connect equipment to the structured cabling sockets, would have no screening / earthing.
There are certain vendors who will provide what they claim to be "screened Ethernet patch cables". Such products are just snake-oil.