Final answer:
John Locke is the Enlightenment philosopher most closely associated with the idea that people have the right to establish a new government if the existing one fails to protect their natural rights, a concept influential in the creation of the Declaration of Independence.
Step-by-step explanation:
The Enlightenment philosopher who would align most closely with the statement "When a government fails to safeguard people's natural rights, individuals have the right to establish a new government" is John Locke.
Locke's political philosophy, particularly as expressed in his 'Two Treatises of Government,' emphasized that individuals possess natural rights to life, liberty, and property, which governments are created to preserve.
When a government fails to protect these natural rights, according to Locke, the people have the authority to overthrow that government and establish a new one that will ensure their rights and liberty.
This notion deeply influenced Thomas Jefferson as he drafted the Declaration of Independence, embedding the idea that it is a government's duty to secure rights, and upon failure to do so, the people have the right and duty to alter or abolish it.