The last stage of material failure often shows a regime with power-law acceleration as the material lifetime is approached. We study this experimentally in tensile creep with paper samples using digital image correlation. The last, tertiary creep stage exhibits scale-free features in the sample response (strain rate) and its fluctuations. It is accompanied by an increasing localization of strain at the location of final failure. The main features are reproduced by a material model built on a viscoelastic fiber bundle model.