In D&D3e, if you successfully hit a target you always did at least 1 point of damage (before applying Damage Resistance), even if you had a Strength penalty. I can't find any mention of that rule in the 5e PHB. Does the rule no longer apply, or did I just overlook it?
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Rounding rules in 5e were a problem since the beginning.
For example, RAW, at level one you do not heal at all from a long rest (half your HD is 0.5 which is rounded down to 0). This issue was addressed here by Mike Mearls, so this time the RAW was actually contradicted.
However, in your case it is correct to say the rule no longer applies. Another tweet (god I wish we had that back in the 90s) clarifies that the minimum is indeed 0.
There is no such rule in 5e.
An unarmed strike by someone (other than a monk) with less than 10 strength will never do any damage, for example.