Could go either way. The seam giving out and vinyl curling is normal wear and tear. However, you may have had a duty to inform landlord about the curling vinyl so he could fix it befor the vinyl was damaged. If you didn't report the seam, the key issue would be whether failing to notify landlord about the seam makes your damaging the vinyl 'negligent' under 76-1421(6). Here's the section of the landlord tenant act in Nebraska.
76-1421. Tenant to maintain dwelling unit.
The tenant shall:
(1) Comply with all obligations primarily imposed upon tenants by applicable minimum standards of building and housing codes materially affecting health or safety;
(2) Keep that part of the premises that he occupies and uses as clean and safe as the condition of the premises permit, and upon termination of the tenancy place the dwelling unit in as clean condition, excepting ordinary wear and tear, as when the tenancy commenced;
(3) Dispose from his dwelling unit all ashes, rubbish, garbage, and other waste in a clean and safe manner;
(4) Keep all plumbing fixtures in the dwelling unit or used by the tenant as clean as their condition permits;
(5) Use in a reasonable manner all electrical, plumbing, sanitary, heating, ventilating, air conditioning and other facilities and appliances including elevators in the premises;
(6) Not deliberately or negligently destroy, deface, damage, impair or remove any part of the premises or knowingly permit any person to do so;
(7) Conduct himself and require other persons on the premises with his consent to conduct themselves in a manner that will not disturb his neighbors' peaceful enjoyment of the premises; and
(8) Abide by all bylaws, covenants, rules or regulations of any applicable condominium regime, cooperative housing agreement, or neighborhood association not inconsistent with landlord's rights or duties.
Source: Laws 1974, LB 293, § 21.
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This is not legal advice and you are not my client. Double check everything with your own attorney and your state's laws.