The SRD has a rule preventing negative damage. Other sources do not specifically mention this case.
The [rules][1]rules in the SRD say:
"With a penalty, it is possible to deal 0 damage, but never negative damage."
SRD PDF (page 96)
However, in the corresponding section in the PHB this sentence is absent. It is also not mentioned in the errata.
Errata, PHB, Version 1.22, 017
However since the SRD is to be seen as a free to use subset of the rules available in the official publications it can be assumed that the rule is meant to be in the official rules but was most likely excluded for formatting purposes.
Other sources of rules are also relatively silent on this matter, the closest Sage Advice states:
There is no damage minimum in the rules, so it is possible to deal 0 damage with an attack, a spell, or another effect.
SA Compendium Version 2.1, 2017
Given the infrequency of negative damage actually occurring, and the SRD having a specific rule about it, it is safe to assume that negative damage just hasn't merited official response. [1]: http://5e.d20srd.org/srd/combat/damageAndHealing.htm#damageRolls"With a penalty, it is possible to deal 0 damage, but never negative damage."