[Petrosius]

This is what happens when you do not teach logic or English grammar. "That to secure these rights" is not a continuation of a list but a subordinate purpose clause: the institution of governments is only for the purpose of securing the unalienable rights endowed by the Creator. The rights of Life, Liberty and the pursuit of Happiness come from God; governments are instituted by Man to secure these rights. This subordination of purpose is the same with or without a period.

[Mr Rogers]

” the institution of governments is only for the purpose of securing the unalienable rights endowed by the Creator”

BINGO!

Governments “deriv[e] their just powers from the consent of the governed” toward the end of securing “the unalienable rights endowed by the Creator” - and any government which fails to secure those rights for the people is illegitimate.

Thus, “whenever any Form of Government becomes destructive of these ends, it is the Right of the People to alter or to abolish it, and to institute new Government”.

Period, comma or simply a dash, the meaning is unchanged. A legitimate government exists by the consent of the governed, and serves a legitimate purpose only so long as it makes it possible for the people to exercise and enjoy “the unalienable rights endowed by the Creator”.