Ask Mr. Smarty Plants

Yucca elata (soaptree yucca), a native of the US desert southwest can grow to 20 feet in height in ideal conditions.  Unlike their cousins the agaves, which flower only once then die, yuccas can and often do flower each year from the same plant.  Under normal circumstanced then, you would not expect your yucca to die now.  However, everything dies sometime and this may be the time for your specimen plant.  In fact, many plants produce flowers and fruit when under stress, or when sick and dying.  Think of it as their last-gasp effort to reproduce before departing this mortal coil.

Another possibility, is that your plant is, as you suggest, simply bedraggled from its flowering efforts.  It is normal for old Yucca elata leaves to die and persist on the plant massing beneath fresh growth.   Flowers generally last a few weeks.  Unless you hand-pollinate the flowers, you're unlikely to see any fruit since yuccas are all naturally pollinated only by certain species of coexisting moths.

As a rule, transplanting suckers or side shoots of Yucca elata is unsuccessful.  They don't actually form bulbils.  Propagation of this species is usually accomplished only by seed.  Since the species is very slow-growing, expect to wait years from sowing seeds or transplanting young seedlings to again enjoy a specimen plant in garden.  There is a good chance, though, that one or both of your existing plants will survive.