Valerie, to try & answer your questions, older balloon-framed homes do often have some floor sagging problems, but from my experience it often has more to do with inadequate or failing support beams & shifting foundations than with the actual framing. The exception to this is that many joists put in these older homes would not meet the standards for today; often having notches cut in the very top or bottom of the joist, or large external knots in the wood which make weak points that can lead to failure of individual joists.
Unless you're speaking of replacing/sistering joists above a finished area, like floor joists of a 2nd story, the process is usually done from below, thus the subflooring would not matter. In the case of a 2nd story or situation where the subfloor did go under the wall framing, the flooring would be cut out next to or near the wall for access, then a mending plate would be added to the bottom of the flooring to support the joint between the original floor & the repair area.
One of the more important "to be conscious of" factors of owning a balloon framed home is fire; those open wall spaces that extend basement to attic with no closure can provide vital oxygen to fuel a fire & allow fire to spread extremely quick. Retrofitting to block the spaces not only protects against this risk, it cuts down the overall air infiltration to the home & makes it possible to have existing uninsulated walls insulated with blown cellulose or other material.