  There is currently much interest in the recycling of entangled systems, for
use in quantum information protocols by sequential observers. In this work, we
study the sequential generation of Bell nonlocality via recycling one or both
components of two-qubit states. We first give a description of two-valued qubit
measurements in terms of measurement bias, strength, and reversibility, and
derive useful tradeoff relations between them. Then, we derive one-sided
monogamy relations for unbiased observables, that strengthen the recent
Conjecture in [S. Cheng {\it et al.}, Phys. Rev. A \textbf{104}, L060201 (2021)
] that if the first pair of observers violate Bell nonlocality then a
subsequent independent pair cannot, and give semi-analytic results for the best
possible monogamy relation. We also extend the construction in [P. J. Brown and
R. Colbeck, Phys. Rev. Lett. \textbf{125}, 090401 (2020)] to obtain (i)~a
broader class of two-qubit states that allow the recycling of one qubit by a
given number of observers on one side, and (ii)~a scheme for generating Bell
nonlocality between arbitrarily many independent observers on each side, via
the two-sided recycling of multiqubit states. Our results are based on a
formalism that is applicable to more general problems in recycling
entanglement, and hence is expected to aid progress in this field.
