Those eligible to become free agents had the right to put themselves on the market at midnight EST Thursday.
To make sure Adams did not do that, the Cowboys signed him to a long-term contract. Terms were not disclosed. Adams has played 10 years the NFL, all of them with Dallas.
The San Francisco 49ers, meanwhile, reportedly signed quarterback Alex Smith through the 2010 season. The San Francisco Chronicle said the deal averages $8.25 million per year and includes $24 million in guaranteed money.
Smith had shoulder surgery in December and threw for just 914 yards in 2007.
In other moves, the St. Louis Rams released Isaac Bruce, the franchise's all-time leading receiver, and Miami signed wide receiver David Kircus.
Kircus did not play in the league last season after being cut by Denver prior to the start of the campaign.
In Houston, the Texans signed wide receiver-kick returner Andre Davis to a new long-term contract. He scored three touchdowns on kickoff returns last year.