Final answer:
Stephen F. Austin led the Old Three Hundred to Texas as part of early colonization efforts, but not all accompanied him initially; many followed due to land opportunities and economic hardship elsewhere. Later, the Mexican law outlawing slavery and subsequent Texas independence saw Texas's population nearly triple, in part through the influx of American slaveholders.
Step-by-step explanation:
Not all of the Old Three Hundred arrived in Texas with Stephen F. Austin. The Old Three Hundred refers to the settlers who received land grants as part of the colonization efforts initiated by Stephen F. Austin in the early 1820s. Austin's role as an empresario allowed him to allocate lands to these families, making them among the first colonizers of Mexican Texas, which later became the state of Texas.
When the Mexican president Vicente Guerrero outlawed slavery in 1829, it was in an attempt to decrease the influence of American settlers, though his decree was not fully enforced in the region that would become Texas. Despite this, the prohibition of slavery was a factor that would eventually contribute to the tension leading up to the Texas Revolution and the formation of the Republic of Texas, more familiarly known as the Lone Star Republic.
It is important to note that after the Texas Revolution in the late 1830s, many Americans, including slaveholders, immigrated to Texas, leading to a population boom. This migration can be attributed to the economic opportunities offered by the new nation and partly triggered by the financial setbacks faced by many during the depression of 1837. The phrase 'Gone to Texas' became popular as a note left behind by those who departed in search of a new beginning.