Severance if I leave?

I have worked at the same plant for 20 years, although it has been sold two times. They have historically (and recently) offered their "enhanced severence package" to employees whose jobs have been eliminated. In January, I applied for an internal position. I was told that if I did not get the position, my job duties would be distributed to the person who did get the job and other current employees as a cost savings move- meaning that at that point I would not have a job. They hired a person from outside the company for the position. In Feb, I asked & was told that there would be no job here for me. I asked when- no answer. I asked about severence & was told I would be eligible for the enhanced package. To date, I have not been given a date of termination. The person I am supposed to be replaced by is here already, and still no end date.
My question is this: since I have been told that my job has been eliminated- in fact they sent out a site-wide e-mail to that effect- if I decide not to sit and wait for them to decide when they are ready for me to go and I find another job, should I expect them to honor the severence agreement? Is it reasonable for them not to give me a termination date? (OK, that is two questions.) The pkg they described to me includes two weeks of salary per year of service, one year of paid health/dental insurance for me & my spouse, $1500 in training, and use of a placement service- a lot of $$ involved. I hate sitting here like a lame duck not knowing I have a job to go to, but I also hate the thought of them getting away with replacing me with a young man and not paying the severance as promised.