Trade agreements do eliminate some jobs, typically those with the lowest (ot lower) economic value. And that does hurt people working low-skilled jobs especially in industries that have stagnated over decades and decades. However, those same people (plus many, many more) benefit from lower prices for certain manufactured goods. As an example, many apparel and accessory companies manufacturer their goods in Asia because labor cost in much lower and the requisite skill level is not very high. This translates into lower consumer retail prices that benefit every US consumer (consider basic apparel and accessories sold at Walmart, Macy's, Amazon, Target, etc -- albeit some of these companies have additional competitive advantages in scale, supply chain management, automation, et al that may result in even lower consumption prices).
Implementing broad tariffs against low wage manufacturers will simply lead to higher prices in the US. Basic economic theory suggests that goods and services requiring low levels of skill will flow to countries that can most effectively compete by supplying acceptable products and services at lower prices -- cotton tee-shirts from Vietnam and customer support call centers in India -- while countries that possess more highly skilled workers and more capital (both intellectual and financial) will focus on producing more complex goods and services. Advanced computer hardware and software, bioengineering, advances in alternative energy, finely produced timepieces in Switzerland, beautifully designed leather goods from France and Italy (this is not to suggest that Europe can only succeed with high-end luxury apparel and accessories).
Free markets typically result in goods and services produced in countries that can do so most efficiently. This in no way excuses dumping products into other markets below cost. And despite the statement that free markets -- and by extension, free trade agreements -- will disperse development and production towards those countries that are most efficient, there will always be certain industries deemed "strategically important" to a host nation, such as the auto industry and ensuing bailout, defense contractors, certain technology firms in the US, where maintaining national production capabilitiy is considered more important than cost or other efficiency.
My recall of my Stanford macro-economics may be off a bit, but I think most of this piece stands. As a country, we must help displaced workers with education, training and job opportunities. As a broad and perhaps poor generation, an Appalachian coal miner may not have the skills or interest to become a software programmer, but we have a crumbling national infrastructure that needs to be fixed. And his/her current skill set, combined with additional training, may be much more transferable towards addressing issues we have at home.
Blanket assertions by politicians will get us nowhere. Trump could launch a massive worldwide recession with his ignorant ideas. But we may be able to count on a near-worthless Congress (House and Senate) to constrain the potential damage. Congress has demonstrated a great ability to get absolutely nothing done, except to exacerbate partisan tensions to the piont that "compromise" is now a damning word. Hell, Reagan and Tip O'Neill had much different priorities, but they were able beneath the headlines to work together at times. Neither of the "presumptive" candidates excites me at all, and the ability of a president to enact meaningful change is overblown, especially when coupled with a completely malfunctioning congress. As I conclude this meandering discourse, I will say the Trump scares the hell out of me. His supposed business 'acumen' won't make him an effective president. Trump runs a private company built by his father, a firm with little oversight, accountability, and a well-hidden track record. He has been most successful as a "barker", marketing himself across licensing deals and a reality TV shoe. I see zero skills transferable to serving as president of the US.