If the wire is run to the fuse box and from there to the ignition, then the section of wire from the battery to the fuse box would be unprotected. With the load this wire must carry, protection is highly recommended. Sometimes on this wire a fuseable link is used instead of a fuse. Fuseable links can be difficult to recognize, often they look like a smaller wire has been spliced into the main wire (look closely for a labeled rating on the link wire). Fuseable links (as any fuse) should be placed close to the source of power, in this case it would be close to the battery or solenoid connection.

Usually the battery wire goes to the ignition switch’s BATTERY terminal, continuing from the ignition switch BATTERY terminal to the FUSE box constant on section. Fuse boxes usually have two (or more) isolated sections, with some sections controlled by the switch.

The constant on section is NOT controlled by the ignition switch, it gets its power from the battery, power is distributed through fuses and this section is usually used for headlights, tail lights, brake lights, horn, exc. (sometimes horn, headlights and other accessories are controlled through relays).

The ignition switch’s STARTER and IGNITION terminals usually connect to the starter SOLENOID and ignition COIL directly, they are usually fused individually (fuseable link wires near the switch). The ignition switch’s IGNITION connection will be on with the STARTER position, but the STARTER connection will NOT be on in the IGNITION position.

The ignition switch’s ACCESSORY terminal connects to the fuse box’s accessory section (isolated section) the power is distributed through fuses to the accessory items such as radio, windows, doors, wipers, exc.. The ignition switch’s ACCESSORY items will be on with the ignition switch’s IGNITION and ACCESSORY positions, but the IGNITION will NOT be on in the ACCESSORY position.

Hopefully this clears it up a little.