  Optical depth variations in the Galactic neutral interstellar medium (ISM)
with spatial scales from hundreds to thousands of astronomical units have been
observed through HI absorption against pulsars and continuum sources, while
extremely small structures with spatial scales of tens of astronomical units
remain largely unexplored. The nature and formation of such tiny-scale atomic
structures (TSAS) need to be better understood. We report a tentative detection
of TSAS with a signal-to-noise ratio of 3.2 toward PSR B1557$-$50 in the second
epoch of two Parkes sessions just 0.36 yr apart, which are the closest-spaced
spectral observations toward this pulsar. One absorption component showing
marginal variations has been identified. Based on the pulsar's proper motion of
14 mas $\rm yr^{-1}$ and the component's kinematic distance of 3.3 kpc, the
corresponding characteristic spatial scale is 17 au, which is among the
smallest sizes of known TSAS. Assuming a similar line-of-sight (LOS) depth, the
tentative TSAS cloud detected here is overdense and overpressured relative to
the cold neutral medium (CNM), and can radiatively cool fast enough to be in
thermal equilibrium with the ambient environment. We find that turbulence is
not sufficient to confine the overpressured TSAS. We explore the LOS elongation
that would be required for the tentative TSAS to be at the canonical CNM
pressure, and find that it is $\sim5000$ -- much larger than filaments observed
in the ISM. We see some evidence of line width and temperature variations in
the CNM components observed at the two epochs, as predicted by models of
TSAS-like cloud formation colliding warm neutral medium flows.
