is the 連用中止法 (i-stem) of ない, the negative form (〜ない) of ある
'without' or 'un-', but still nominalising the noun.
It's an old form, that has been largely replaced by ない.
Note that it can be attached to nouns directly:
酸素無しでは 生きていけない。 You can't live without oxygen
休日なしで働く Working without taking a holiday.
砂糖なしケーキ A cake without sugar.
話したりも無しに休まれては困るね。 To be stressed because someone took a day off without even telling you.