Would like to work and live in Ecuador

To work and live ongoingly in Ecuador, you would need a residency visa.

It may be possible, if you have a job offer, to obtain a non-immigrant work visa.  The Cancillería would want to see a written formal contract stating the position you have been offered.

Why don't you review the visa requirements at the link below, and post again with more information about yourself:  your travel background, why you want Ecuador, your job or professional experience, your degree of fluency in español, your willingness to visit Ecuador to see if it is right for you, your family (if any) that would move with you, whether you would invest in a bank CD if necessary to obtain an Ecuadorian residency visa?

  www.cancilleria.gob.ec/visas-inmigrante/?lang=en
(Click on the green language icon for English option if the site comes up in Spanish.)

cccmedia in Quito