Different ways to paint inside of a shape that is not closed

Question

1. One segment of a path is not closed and I want to fill the shape with a color. How would you handle this? Just draw a line and join it together with the rest of the shape so you can apply a fill? OR would you do this differently?
2. Isn't there some tool that also allows you to paint inside shapes that are not closed?
Thanks.

Answer 1

function(){return A.apply(null,[this].concat($A(arguments)))}
So is the whole idea behind Live Paint that it will somehow complete a shape with paint even if the path is not there?
No. The paths have to "be there." The whole idea of Live Paint is to allow the user to apply fills and strokes according to what visually appears to be contiguous bounds of filled/unfilled and/or colored/uncolored regions. In other words, to apply fills and strokes as if the visual appearance of paths actually were the shapes of the paths.
Example 1:
Draw a tic-tac-toe board. Four stroked unfilled open paths. Now you know these paths are not connected, and there is no actual rectangular closed path in the middle "square" to which you can apply a normal fill. But the four strokes appear to form a square that you could fill. LivePaint acts as if that square was there, and fills it. (Under the table, LivePaint is actually creating a "virtual" or "live" rectangle that corresponds to the visible white space surronded by your original four paths. You can see this by Expanding the LivePaint group.)
Example 2:
Draw two partially-overlapping unstroked circles with the same solid fill. Now you know these two circles are separate paths; there is no actual "figure 8" path. But there appears to be a figure 8 -shaped path just because the two circles have same-colored fills. LivePaint can act as if that "figure 8" path is actually there, and fill it all at once (by doubleClicking). In this case, the expanded result will be three separate closed paths with the same fill, not one figure 8-shaped path. So now instead of having two overlapping paths that look like a single figure 8 path, you have three non-overlapping paths that look like a figure 8-shaped path.
So LivePaint does act upon paths that "are there." It performs path-combination operations to create new paths (sort of like Pathfinders) based upon the stroke and/or fill "boundaries" that you visually see; but it does so in a "live" fashion, in an attempt to make it feel more like flood-filling in a raster image program, and in an attempt to make the auto-created shapes themselves remain "live" even as you alter the original paths.
Sometimes its behavior is intuitive. Other times, it is not.
Illustrator is neither the first nor the only vector drawing program to provide this kind of function. Other vector drawing programs provide flood-fill and flood-stroke features, but do so in a more straightforward manner, not overly-complicating (and confusing) the matter by trying to make too much a "live effect." Illustrator sometimes tends to go overboard with the whole "live effect" thing, and the result is a feature ostensibly designed to make the program more "intuitive" for newcomers, yet becomes more confusing.
Regardless whether you use "live" effect features or not, a serious vector illustrator needs to know what objects will ultimately and actually exist, especially when destined for commercial print. That is, in Example 2, it's up to the user to decide whether it's more appropriate to the intended purpose to end up with two separate overlapping paths that look like a single figure 8, three separate "kissing" paths that look like a figure 8, or one path that actually is in the shape of a figure 8. That's why I've never been particularly enamoured with features like LivePaint. They encourage newcomers to disregard how things are actually built in favor of what things merely "look like" on screen.
JET