A possible identification, and possibly the most accurate, would be the pseudoscorpion. These are commonly referred to as a false scorpion or book scorpion. They are arachnids belonging to the family of pseudoscorpionida. They generally feed on moth larvae, beetle larvae, booklice, ants, mites and small flies. Due to their size it's rare for people to spot pseudoscorpions, however they are harmless to humans. The abdomen of arachnid is short and rounded at the rear, rather than a tail and stinger like scorpions do. They have eight legs and two very long palpal chelae (pincers), which resemble those of a scorpion. These may be compared to crab claws also. Chelifer cancroides are the species of pseudoscorpian most commonly found in homes. They feed on dust mites and booklice apparent in households and enter by riding with other insects or bugs. It is possible that the spiders found dead are a coincidence rather than the presence of a pseudoscorpion in the household having an influence.
There are many forms of tick that have crab-like claws and are commonly very small in size. These are also usually very small and don't just feed on the blood of dogs and deer. They usually have a more rounded body rather than flat, however and don't feed on spiders.
There are methods for identifying unknown species. This can be done online using many websites or by attempting to capture the creature and consulting a specialist.