Heal broken stems with a drinking straw. Split the straw lengthwise and cut to the desired length. Carefully put it around the broken stem and tape it shut. Make sure to water the plant well. Then hope for the best. This quite often will give the stem the support it needs to heal.
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You can replace the stem of a flower that has broken off with a straw, the way florists sometimes do. This also works for the heads of artificial flowers. I just put a stem on a flower that I had scavenged off a wreath so I could put it in a ceramic vase the hubby gave me for my birthday.