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How much water is the plant getting?  The easiest way to kill is a succulent is to over-water!  Aloe plants are generally very easy to care for, but care should be taken to avoid overwatering. The plants should be watered deeply but allowed to dry out before the next watering. Check the soil prior to watering. Allow the soil to dry down to a depth of 7.5 to 10 cm (3-4 in) for older, well-established plants or 3.5-5 cm (1-2 in) for younger plants. The plant could also be limp because it got exposed to extremely cold temperatures even for a short time.  In addition, although Aloe plants require lots of lights, sitting them in full sun can be harmful and it is best to position potted Aloes in a bright window. If the plant is receiving too much sun, the leaves will begin to turn brown.  It may be that your plant has:

Soft rot

• Cause: Temperature 25-35 C, high humidity, waterlogged soil and excess nitrogen fertilizer, enters through damaged leaves.
• Treatment: Prevention rather than cure. Avoid excess fertilizer, overwatering or watering from above and damage to foliage. Saving an infested plant tends to be unpractical, but you can try and remove infected tissues whilst removing and replanting in a sunnier location.

References

Aloe pests and diseases - Discover | Candide Gardening

Succulents handout.pdf (msu.edu)

Aloe vera | Diseases and Pests, Description, Uses, Propagation (psu.edu)
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