Frames that are not tagged on a trunk are in the native VLAN, which is usually VLAN 1. The tags on a trunk are to allow a device on the other end to differentiate which frames belong to which VLAN. That means that one VLAN can send untagged frames. That VLAN is called the native VLAN, and the receiving switch knows that any untagged frames received on an interface blong to the native VLAN.
Also, understand that the hosts send and receive untagged frames (most hosts do not understand VLAN tags and will drop tagged frames). The access interfaces on a switch do not tag the frames. Tags are only used on trunks where there may be multiple VLANs, but that is not the case for access interfaces.
The router will create the frames for the correct VLAN based on the destination address. If a packet coming into the router is destined for an untagged VLAN on the router interface, then the router will not place a tag on the frame containing that packet, but if the packet is destined for a VLAN that is tagged on the router interface, then the router will place a tag on the frame containing that packet.