My agave has black tar like substance in the center of the plant and one of the leaves has suddenly become limp.
This symptom worries me - this is most likely some kind of rot, and as it's in the center of the rosette, it's most likely pretty well through the whole crown of the plant.
If you've had a lot of rain, and then hot weather, this can cause this type of damage. If you have some pups forming at the base of the plant, it might be worth attempting to propagate them, due to the high risk of them getting some kind of rot too.
If possible, I would try and cut out the damaged leaves - this may cause a whole other issue, where the growing point of the plant might be removed. However, this might encourage it to form pups right away if it hasn't already.
It's hard to tell from your picture if this is a potted plant, or growing outdoors. If it's outside planted in the ground, I would make sure to add some lava rock, small gravel or other well drained material to the planting area if you want to try and keep growing these types of plants in your climate.
High humidity, combined with heat and excess moisture is bound to kill these drought loving plants. Try and copy their native habitat for the best results.
Best of luck with your Agave.
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