  Strange hadron production in pp collisions at $\sqrt{s}~=~7$ TeV is studied
in jets and underlying events using the PYTHIA8 event generator. Matching
strange hadrons to the jet area and the underlying event area is expected to
help us disentangle the strange particles produced in hard and soft processes.
The yield and the relative production of strange hadrons dependent on the event
multiplicity are investigated with the color reconnection and color rope
mechanisms implemented in the PYTHIA8 framework. It is found that the inclusive
strange hadron productions can be reasonably described by the color
reconnection and color rope combined effects. A significant multiplicity
dependent enhancement of the strange baryon production in the jet area is
observed induced by the modified string fragmentation mechanisms, indicating
the strange baryon enhancement persists in both the hard and the soft process.
Multi-strange baryons are found to be more collimated with the jet axis than
other strange hadrons in the string fragmentation picture with the jet shape
analysis technique. Future experimental examination of these jet related
strange hadron productions will provide more insight to the origin of
strangeness enhancement in small systems.
