I think those are fragments of the plastic liner. If the residue comes from the sea surface, the little fibrous objects may be "microplastics"

please check the link below:

http://rsos.royalsocietypublishing.org/content/1/4/140317

http://www.deepseadrilling.org/05/volume/dsdp05_23.pdf

Regarding the fact, that the fibrous material is from tho whole core (enriched in severeal layers or +- equally distributed?) and if you can exclude contamination (which is the most reliable information, regarding Renata's answer), you may check if they are polymers or silicones, and if, what type.

It may sound strange, but take in regard that meteorite impacts (exploding subaerial of in contact with water) can form silikone and polymer fibres:

Hochstim 1963 HYPERSONIC CHEMOSYNTHESIS AND POSSIBLE FORMATION OF ORGANIC COMPOUNDS FROM IMPACT OF METEORITES ON WATER. PNAS 50(2): 200–208. 

Adadurov et al 1972 Shock-initiated polymerization of acrylamide. Combustion, Explosion and Shock Waves Volume 8, Issue 4, pp 465-467.

Mimura 1995 Synthesis of polycyclic aromatic hydrocarbons from benzene by impact shock: Its reaction mechanism and cosmochemical significance. Geochimica et Cosmochimica Acta Volume 59, Issue 3, February 1995, Pages 579–591

Matthews & Minard 2006 Hydrogen cyanide polymers, comets and the origin of life.Faraday Discuss. 2006;133:393-401; discussion 427-52.

Dremin & Babare. ON THE SHOCK POLYMERIZATION PROCESS. Journal de

Physique Colloques, 1984, 45 (C8), pp.C8-177-C8-186.

Courty & Martinez 2015 Terrestrial Carbonaceous Debris Tracing Atmospheric Hypervelocity-Shock Aeroplasma Processes. Procedia Engineering

Volume 103, 2015, Pages 81–88

You may check this.

 I will agree with Renata. they look like the small cut pieces from the plastic liner of the core. I personally experienced the same in several sediment cores after we split them.   it depends on the type of the plastic of course, they are cut like this during the cuting and splitting process. once you cut the liner/tube there are always small plastic pieces everywhere and if you used a nylon thread (fishing line is usually used to split the sediment) they are spread everywhere on the surface of the split halves. To be sure I would suggest to take small samples avoiding the egdes/plastic liner and check the sediment itself. 

Yes, core liner fragments, especially if they are stiff and somewhat helical, as they appear to be.

Thank you everyone for your suggestion, I think some spot analysis will help me to check what exactly these objects are.

The material appears to be polyethylene material fibers. You need to know if these materials are rigid and which caracterize the polyethyçene materials.

Yeah. It looks like plastic liners only. I observed on many of the cores while washing samples for foraminifera separation and under microscope. It indicates that during cutting and splitting the core pipes these fibrous fragments get included within the outer sediment surface.

What you can do is- Observe the core section carefully along the cut section after splitting. If you see such particle accumulation simply scratch the outer layer of sediments perpendicular to the pipe so that there is no downcore mixing of the sediments and remove the plastic fibers.

My experience in working deep-sea sediment cores suggest that those are fragments of core liner, period.

Thank you everyone for your valuable suggestion, it was of great help.