A sediment filter, not a safety fence
People often lump silt fence in with the orange plastic fencing that shows up around a job site, since both arrive on stakes before anything else happens. They do different jobs. Orange construction fencing marks a boundary and keeps people and vehicles out of a work area. Silt fence is a filter: the woven fabric lets water pass through slowly while it holds back the dirt the water was carrying. One is about site safety and access. The other is about keeping mud out of the ditch, the neighbor's yard, and the storm drain down the hill.
Where it goes and how long it stays up
On a site with any real grading or excavation, silt fence runs along the low side of the disturbed ground, staked into the soil with the bottom edge of the fabric trenched in so water cannot just slide underneath it. It stays up through excavation, base work and the pour itself, because that is when bare dirt is most exposed and most likely to wash. Once grass or gravel is established and the ground around the new slab has settled, it comes down. A small driveway or patio job might need a short run of fence at one low corner. A larger site with more grading can need it wrapped around most of the low side of the lot.
Whether your job needs one
Not every pour disturbs enough ground to need it. A small patio replacing an existing slab in the same footprint is a different situation from a new driveway cut into a slope, where a good amount of dirt gets moved and graded before any stone or concrete goes down. Whether your site calls for silt fence comes down to how much ground gets disturbed and what your county wants for that scope of work. That is worth asking about at the estimate, along with everything else site prep involves.