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To replace the missing bolt, first drill through the metal bracket. Make sure not to drill through the wood behind it.
If attempting to drill the bolt straight through, there may be a chance of fracturing the wood. Drill a pilot hole first to avoid this problem. When choosing the site of the new pilot hole, make sure that it's not too close to the old pilot hole. When choosing a drill bit, use a half size smaller than the bolt. In this case, use 1/8". Drill a hole no more than the depth of the bolt.
Drive a new 1/4" lag bolt into the new framing. Drive it in slowly to avoid the wood splitting. Don't tighten the bolt too much to avoid shearing off the head of the bolt. Use a socket wrench when working in this tight area.
Hide the old hole by filling it in with wood putty and paint over it.
To secure the stair railing, drill into the stair stinger at a site where the wood isn't cracked and still has some integrity to it. Use a rafter angle square to drill at a perfect 90 degree angle.