Tried to destroy a wooden slab wich took forever with an axe but with a pickaxe it was instant. After getting the slab into my inventory the texture was broken.
Normal wood slabs have the ID 126, but the items you are showing actually have the ID 44:2. 126 is associated with wooden slabs, but 44 belongs to stone slabs (for example, cobble slabs are 44:3). "Wooden Slab"s were officially replaced with "Oak Wood Slab"s in 1.3.1, if I recall correctly. However, existing slabs were not converted. I don't know where you found that slab, but it dates back to 2012. They are actually still pretty common (especially in old towns), I have a few stacks of them as well. The TL;DR: Those slabs were Minecraft's prototypes for wooden slabs in 2011 and 2012 and are essentially stone slabs with a plank texture.
