It does make sense if the line Y=mX-c. The y intercept is -c and the slope m is a positive fraction, for example ⅓, because the length of the foot is always less than the height of the whole body. A line extends to infinity in both directions, but the data only occupy a segment of the line. There is no meaning attached to Y=0, implying no feet, so no height X=c/m. (If m=⅓, X=3c, which is a measurable height, but having no feet!)
The regression line is only a model of the data available and the range of applicability is limited.
EXAMPLE
Suppose for X=66” Y=10” and X=72” Y=14” we have m=⅔ and c=-34”, so Y=⅔X-34. We have a negative y intercept. So it would appear that when X=51” Y=0. But the dataset doesn’t include this low value of X, so the value is outside the domain of the given data. The line is a best fit for the given data only.