Why did the spider die?

One way is to soak the end of a Q-tip in water and then put the wet end in front of the spider. If the spider is thirsty it will come up to the Q-tip and suck water out of it. A similar method is to use a cotton ball, although wet cotton balls are more unwieldy to handle. You can also take a plant mister and just spray some drops of water near it, although this can startle the spider and cause it to run away. A dish of water might work, but if the spider is really weak it might accidentally drown.