What signals a ribosome to stop production when the cell is out of available amino acids?
When cells run out of amino acids, more and more of their tRNAs remain uncharged. This elevated ratio of uncharged/charged tRNAs trigger complex signalling pathways that control amino acid biosynthesis, general reduction of translation, halting ribosome biosynthesis, autophagy (includes ribophagy - digestion of ribosomes) to recycle cells' components, etc. This can be clubbed into general amino acid control (GAAC) and involves the super important regulatory kinase protein called as Target of Rapamycin (TOR) and other transcription factors. The regulation of amino acids level is one of the most basic and important features of cellular metabolism and can be found conserved from yeast to humans. In addition to GAAC, there can be pathways for some specific amino acids as well.

There is not shortage of scientific literature. To start with you can read following article:

http://www.cell.com/trends/cell-biology/abstract/S0962-8924(14)00036-1
http://jcb.rupress.org/content/206/2/173.full