  The James Webb Space Telescope (JWST) has recently uncovered the presence of
low-luminosity active galactic nuclei (AGNs) at $z=4-11$. Spectroscopic
observations have provided estimates of the nuclear black hole (BH) masses for
these sources, extending the low-mass boundary down to $M_{\rm BH} \sim
10^{6-7}~M_\odot$. Despite this breakthrough, the observed lowest mass of BHs
is still $\gtrsim 1-2$ orders of magnitude heavier than the predicted mass
range of their seed population, thereby leaving the initial mass distribution
of massive BHs poorly constrained. In this paper, we focus on UV-to-optical (in
rest frame) flares of stellar tidal disruption events (TDEs) embedded in
low-luminosity AGNs as a tool to explore low-mass BH populations with $\lesssim
10^{4-6}~M_\odot$. We provide an estimate of the TDE rate over $z=4-11$
associated wth the properties of JWST-detected AGN host galaxies, and find that
deep and wide survey programs with JWST and Roman Space Telescope (RST) can
detect and identify TDEs up to $z\simeq 4-7$. The predicted detection numbers
of TDEs at $z>4$ in one year are $N_{\rm TDE} \sim 2-10~(0.2-2)$ for the
JADES-Medium (and COSMOS-Web) survey with JWST, and $N_{\rm TDE} \sim
2-10~(8-50)$ for the Deep (and Wide) tier of the High-latitude Time Domain
Survey with RST. We further discuss the survey strategies to hunt for the
transient high-redshift TDEs in wide-field surveys with RST, as well as a joint
observation campaign with the Vera C. Rubin Observatory for enhancing the
detection number. The high-redshift TDE search will give us a unique
opportunity to probe the mass distribution of early BH populations.
