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We study the properties, connectivity, and galaxy content of groups and filaments in the low-density region (cocoon) around A2142 supercluster (SClA2142). We traced the SClA2142 cocoon boundaries by the lowest luminosity-density regions that separate SClA2142 from other superclusters. We determined galaxy filaments and groups in the cocoon and analysed the connectivity of groups, the high density core (HDC) of the supercluster, and the whole of the supercluster. We compared the distribution and properties of galaxies with different star-formation properties in the supercluster and in the cocoon. SClA2142 and the long filament that is connected to it forms the longest straight structure in the Universe detected so far, with a length of $75$ $h^{-1}$ Mpc. The connectivity of the supercluster is C = 6 - 7; poor groups have C = 1 - 2. Long filaments around the supercluster's main body are detached from it at the turnaround region. Galaxies with very old stellar populations lie in systems across a wide range of richness from the richest cluster to poorest groups and single galaxies. They lie even at local densities as low as $D1 < 1$ in the cocoon and up to $D1 > 800$ in the supercluster. Recently quenched galaxies lie in the cocoon mainly in one region and their properties are different in the cocoon and in the supercluster. The star-formation properties of single galaxies are similar across all environments. The collapsing main body of SClA2142 with the detached long filaments near it are evidence of an important epoch in the supercluster evolution. Further studies are needed to understand the reasons of similarity of galaxies with very old stellar populations in extremely different environments. The presence of long, straight structures in the cosmic web may serve as a test for cosmological models.