Without seeing a picture, I'll recommend soaking in some thin CA. I'm presuming the paper is "delaminating" which can happen in some cases. Thin CA will wick in and hold it together. You might ever so slightly dampen the paper with water or simply breath through the tube a few times to humidify it before applying the CA, as water accelerates the bond. By dampen, I mean take a paper towel, wet it, squeeze all the water out until no more drips, then rub it once on the paper tube where this is happening. Tiny traces of water will adhere to the tube paper, and speed the cure.
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