My approach is to plan as much as is possible the path in which the cable will be run before cutting any holes. A D'versibit might work well to drill a hole from your planned box location to the basement. Planning would include looking at the situation in the attic and locating the place in the basement overhead that is directly under the planned box location. The absence of such concepts suggests that this job should be contracted to a professional. Here is a link that might be useful: D'versibit

I'll go out on a short limb for you as I do not know the 'official' answer since this is actually a building code question; not an electrical one. However, assume you take worse case scenario and completely remove the whole bottom plate between the studs (e.g. essentially what happens when oval ductwork is installed, right?) Are you left with a significantly less structurally sound wall? Not likely as long as it isn't in the last cavity of the wall or you don't have to remove any lateral blocking. The vertical loads are transfered along the sole plate evenly into the floor underneath. Therefore, drill them as big as you want since anything less than the full width of the stud is still transfering the minute horizontal shear loads - just use strike plates as required.

The code requirements for fireblocking can be found in the International Residential Code, which is the model code used for one- and two-family dwelling construction throughout most of the US. The code states the following: R602.8 Fireblocking required. Fireblocking shall be provided to cut off all concealed draft openings (both vertical and horizontal) and to form an effective fire barrier between stories, and between a top story and the roof space. Fireblocking shall be provided in wood-frame construction in the following locations. 1. In concealed spaces of stud walls and partitions, including furred spaces and parallel rows of studs or staggered studs; as follows: 1.1. Vertically at the ceiling and floor levels. 1.2. Horizontally at intervals not exceeding 10 feet (3048 mm). 2. At all interconnections between concealed vertical and horizontal spaces such as occur at soffits, drop ceilings and cove ceilings. 3. In concealed spaces between stair stringers at the top and bottom of the run. Enclosed spaces under stairs shall comply with Section R311.2.2. 4. At openings around vents, pipes, ducts, cables and wires at ceiling and floor level, with an approved material to resist the free passage of flame and products of combustion Products that can be used for fireblocking, as tested and certified by the ICC Evaluation Service, include Hilti CF810 Fireblocking foam, Dow Great Stuff (orange) fireblocking foam, and others. When evaluating a product for this application, look at the label to see if it mentions ICC-ES and fireblocking.

NEC 300.4 Protection Against Physical Damage. (F) Cables and Raceways Installed in Shallow Grooves. Cableor raceway-type wiring methods installed in a groove, to be covered by wallboard, siding, paneling, carpeting, or similar finish, shall be protected by 1.6 mm (1/16 in.) thick steel plate, sleeve, or equivalent or by not less than 32-mrn (1 1/4-in.) free space for the full length of the groove in which the cable or raceway is installed. Exception No.1: Steel plates, sleeves, or the equivalent shall not be required to protect rigid metal conduit, intermediate metal conduit, rigid nonmetallic conduit, or electrical metallic tubing. Exception No.2: A listed and marked steel plate less than 1.6 mm (1/16 in.) thick that provides equal or better protection against nail or screw penetration shall be permitted. http://freenec.com/T104.html