The fact that Linda finds the rubber hose and understands that Willy is contemplating suicide also serves as a foreshadowing of what actually happens at the end of the play. This foreshadowing was probably a more important consideration in Arthur Miller's view than the effect it has in revealing Linda's character. The rubber hose had to be somehow shown to the audience, and this may have been the best way Miller could think of to do it. The hose had to be shown and some dialogue was necessary to explain to the audience what it signified. The playwright also establishes that Willy has smashed up his car several times, either deliberately or accidentally, but this is not something that can be shown on a stage, whereas a rubber hose is a very easy prop to use.
The dialogue establishes that Willy has been making payments on a $20,000 term life insurance policy for many years. Life insurance policies typically carry an exclusion clause which states that there will be no payment for suicide if it occurs within the first two years of issuance of the policy. This assures the audience that Willy's beneficiary will have no trouble collecting the $20,000 any time Willie decides to end his life. The audience is led to anticipate his suicide by all this foreshadowing. He soliloquizes about suicide, talks to his brother about it, and talks to his neighbor Charley about it. The title "Death of a Salesman" is further assurance that Willy's death is inevitable.
This tells us that Linda loves Willy deeply but is also unable to ever go against anything that he does, even when he is trying to kill himself. Of course she is to be applauded for loving her husband and being so loyal, but she does take it too far. She thinks that to back him up in everything he does is her whole duty but actually she could have served him better by sometimes pointing out where he goes wrong, instead of helping to perpetuate his delusions. She never questions anything he does. Maybe the whole family would have been better off if she had.