Union secretary Tane Phillips said the threat has had a devastating impact on members and their whanau.
"This is an absolute punch in the guts for a group of workers who have already been locked out of their jobs without pay. I've had members call me saying they feel sick to their stomach, they feel like the company is going after their families."
"We are not going to be intimidated by expensive lawyers or bully-boy threats. All we are asking for is for our pay to keep up with inflation. Essity is a large and very profitable company that can easily afford it."
Union member Bill George said the legal threats are "a real a kick in the teeth".
"I'm the only breadwinner and I have a wife as well as two grandkids with disabilities to provide for. We're already hurting from the lockout, and now the company wants to sue us for thousands. I just ask where their humanity is."
Essity is a Swedish-based multinational company that made $1.8 billion of profit globally last year. Its brands in New Zealand include Purex, Sorbent, Libra and Handee.