For example ...

We had some faild builds.
After fixes the build was now OK but the mail notification is failing !!!

ERROR: Failed to set Jenkins Identity header on email.
java.lang.NullPointerException
at org.jenkinsci.main.modules.instance_identity.InstanceIdentity.get(InstanceIdentity.java:126)
at jenkins.plugins.mailer.tasks.MimeMessageBuilder.setJenkinsInstanceIdent(MimeMessageBuilder.java:184)
at jenkins.plugins.mailer.tasks.MimeMessageBuilder.buildMimeMessage(MimeMessageBuilder.java:162)
at hudson.tasks.MailSender.createEmptyMail(MailSender.java:391)
at hudson.tasks.MailSender.createBackToNormalMail(MailSender.java:201)
at hudson.tasks.MailSender.createMail(MailSender.java:192)
at hudson.tasks.MailSender.run(MailSender.java:107)
at hudson.tasks.Mailer.perform(Mailer.java:141)
at hudson.tasks.BuildStepCompatibilityLayer.perform(BuildStepCompatibilityLayer.java:74)
at hudson.tasks.BuildStepMonitor$1.perform(BuildStepMonitor.java:20)
at hudson.model.AbstractBuild$AbstractBuildExecution.perform(AbstractBuild.java:770)
at hudson.model.AbstractBuild$AbstractBuildExecution.performAllBuildSteps(AbstractBuild.java:734)
at hudson.model.Build$BuildExecution.post2(Build.java:183)
at hudson.model.AbstractBuild$AbstractBuildExecution.post(AbstractBuild.java:683)
at hudson.model.Run.execute(Run.java:1743)
at hudson.model.FreeStyleBuild.run(FreeStyleBuild.java:43)
at hudson.model.ResourceController.execute(ResourceController.java:89)
at hudson.model.Executor.run(Executor.java:240)
ERROR: Publisher hudson.tasks.Mailer aborted due to exception
java.lang.NullPointerException
at javax.mail.internet.InternetAddress.toString(InternetAddress.java:461)
at javax.mail.internet.InternetAddress.toString(InternetAddress.java:426)
at javax.mail.internet.MimeMessage.setAddressHeader(MimeMessage.java:707)
at javax.mail.internet.MimeMessage.setReplyTo(MimeMessage.java:694)
at jenkins.plugins.mailer.tasks.MimeMessageBuilder.buildMimeMessage(MimeMessageBuilder.java:175)
at hudson.tasks.MailSender.createEmptyMail(MailSender.java:391)
at hudson.tasks.MailSender.createBackToNormalMail(MailSender.java:201)
at hudson.tasks.MailSender.createMail(MailSender.java:192)
at hudson.tasks.MailSender.run(MailSender.java:107)
at hudson.tasks.Mailer.perform(Mailer.java:141)
at hudson.tasks.BuildStepCompatibilityLayer.perform(BuildStepCompatibilityLayer.java:74)
at hudson.tasks.BuildStepMonitor$1.perform(BuildStepMonitor.java:20)
at hudson.model.AbstractBuild$AbstractBuildExecution.perform(AbstractBuild.java:770)
at hudson.model.AbstractBuild$AbstractBuildExecution.performAllBuildSteps(AbstractBuild.java:734)
at hudson.model.Build$BuildExecution.post2(Build.java:183)
at hudson.model.AbstractBuild$AbstractBuildExecution.post(AbstractBuild.java:683)
at hudson.model.Run.execute(Run.java:1743)
at hudson.model.FreeStyleBuild.run(FreeStyleBuild.java:43)
at hudson.model.ResourceController.execute(ResourceController.java:89)
at hudson.model.Executor.run(Executor.java:240)
Finished: FAILURE

Workaround: downgrade to Mailer 1.12