Step 1: Concept
Determine the number of unpaired electrons using the electronic configuration and Hund's rule.
Step 2: Meaning
Unpaired electrons are found in orbitals that are only partially filled.
Step 3: Analysis
$P^{3-}$ has 18 electrons ($3p^{6}$), all paired. $S$ has 16 electrons ($3p^{4}$), resulting in 2 unpaired electrons. $Cl$ has 17 electrons ($3p^{5}$), resulting in 1 unpaired electron. $Al^{3+}$ has 10 electrons ($2p^{6}$), all paired.
Step 4: Conclusion
Sulfur (S) contains the highest number of unpaired electrons (2) among the given choices.
Final Answer: (B)